@INPROCEEDINGS{Adco1307:Overcoming,
AUTHOR="Ben Adcock and Anders Hansen and Clarice Poon and Bogdan Roman",
TITLE="Overcoming the coherence barrier in compressed sensing",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="1-4",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="coherence, multilevel sampling, asymptotic sparsity, compressed sensing",
ABSTRACT="We introduce a mathematical framework that bridges a substantial gap
between compressed sensing theory and its current use in real-world
applications. Although completely general, one of the principal
applications for our framework is the Magnetic Resonance Imaging (MRI)
problem. Our theory provides a comprehensive explanation for the abundance
of numerical evidence demonstrating the advantage of so-called variable
density sampling strategies in compressive MRI. Another important
conclusion of our theory is that the success of compressed sensing is
resolution dependent. At low resolutions, there is little advantage over
classical linear reconstruction. However, the situation changes
dramatically once the resolution is increased, in which case compressed
sensing can and will offer substantial benefits."
}
@INPROCEEDINGS{Bah1307:Construction,
AUTHOR="Bubacarr Bah and Jared Tanner",
TITLE="On construction and analysis of sparse matrices and expander graphs with
applications to {CS}",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="5-8",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Algorithms, compressed sensing, sparse random matrices, expander graphs",
ABSTRACT="We revisit the probabilistic construction of sparse random matrices where
each column has a fixed number of nonzeros whose row indices are drawn
uniformly at random. These matrices have a one-to-one correspondence with
the adjacency matrices of lossless expander graphs. We present tail bounds
on the probability that the cardinality of the set of neighbors for these
graphs will be less than the expected value. The bounds are derived through
the analysis of collisions in unions of sets using a dyadic splitting
technique. This analysis led to the derivation of better constants that
allow for quantitative theorems on existence of lossless expander graphs
and hence the sparse random matrices we consider and also quantitative
compressed sensing (CS) sampling theorems when using sparse non mean-zero
measurement matrices."
}
@INPROCEEDINGS{Giry1307:OMP,
AUTHOR="Raja Giryes and Michael Elad",
TITLE="{OMP} with Highly Coherent Dictionaries",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="9-12",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="OMP, mutual-coherence, linear dependencies, sparse representations",
ABSTRACT="Recovering signals that has a sparse representation from a given set of
linear measurements has been a major topic of research in recent years.
Most of the work dealing with this subject focus on the reconstruction of
the signal's representation as the means to recover the signal itself. This
approach forces the dictionary to be of low-coherence and with no linear
dependencies between its columns. Recently, a series of contributions show
that such dependencies can be allowed by aiming at recovering the signal
itself. However, most of these recent works consider the analysis
framework, and only few discuss the synthesis model. This paper studies the
synthesis and introduces a new mutual coherence definition for signal
recovery, showing that a modified version of OMP can recover sparsely
represented signals of a dictionary with very high correlations between
pairs of columns. We show how the derived results apply to the plain OMP."
}
@INPROCEEDINGS{Kaba1307:Recovery,
AUTHOR="Maryia Kabanava and Holger Rauhut",
TITLE="Recovery of cosparse signals with Gaussian measurements",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="13-16",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="This paper provides theoretical guarantees for the recovery of signals from
undersampled measurements based on $\ell\_1$-analysis regularization. We
provide both nonuniform and stable uniform recovery guarantees for Gaussian
random measurement matrices when the rows of the analysis operator form a
frame. The nonuniform result relies on a recovery condition via tangent
cones and the case of uniform recovery is based on an analysis version of
the null space property."
}
@INPROCEEDINGS{Mrou1307:Q,
AUTHOR="Youssef Mroueh and Lorenzo Rosasco",
TITLE="q-ary compressive sensing",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="17-20",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="compressive sensing; quantization; 1-bit CS;",
ABSTRACT="We introduce q-ary compressive sensing, an extension of 1-bit compressive
sensing. The recovery properties of the proposed approach are analyzed both
theoretically and empirically. Results in 1-bit compressive sensing are
recovered as a special case. Our theoretical results suggest a trade- off
between the quantization parameter q, and the number of measurements m, in
the control of the error of the resulting recovery algorithm, as well its
robustness to noise."
}
@INPROCEEDINGS{Stoj1307:Low,
AUTHOR="Holger Rauhut and Reinhold Schneider and Zeljka Stojanac",
TITLE="Low-rank Tensor Recovery via Iterative Hard Thresholding",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="21-24",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="tensors; compressive sensing; iterative hard thresholding;",
ABSTRACT="We study recovery of low-rank tensors from a small number of measurements.
A version of the iterative hard thresholding algorithm (TIHT) for the
higher order singular value decomposition (HOSVD) is introduced. As a first
step towards the analysis of the algorithm, we define a corresponding
tensor restricted isometry property (HOSVD-TRIP) and show that Gaussian and
Bernoulli random measurement ensembles satisfy it with high probability."
}
@INPROCEEDINGS{Nguy1307:Finite,
AUTHOR="Truong Thao Nguyen",
TITLE="Finite-power spectral analytic framework for quantized sampled signals",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="97-100",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="To be accurate, the theoretical spectral analysis of quantized sequences
requires that the deterministic definition of power spectral density be
used. We establish the functional space foundations for this analysis,
which remarkably appear to be missing until now. With them, we then shed
some new light on quantization error spectra in PCM and ΣΔ modulation."
}
@INPROCEEDINGS{Chou1307:Non,
AUTHOR="Evan Chou",
TITLE="{Non-Convex} Decoding for Sigma Delta Quantized Compressed Sensing",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="101-104",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Compressed sensing; quantization; Sobolev dual; nonconvex",
ABSTRACT={Recently G\{"}unt\{"}urk et al. showed that $\Sigma\Delta$ quantization is
more effective than pulse-code modulation (PCM) when applied to compressed
sensing measurements of sparse signals as long as the step size of the
quantizer is sufficiently fine. PCM with the $l^1$ decoder recovers an
approximation to the original sparse signal with an error proportional to
the quantization step size. For an $r$-th order $\Sigma\Delta$ scheme the
reconstruction accuracy can be improved by a factor of
$(m/k)^{\alpha(r-1/2)}$ for any $0 < \alpha < 1$ if $m \gtrsim k(\log
N)^{1/(1-\alpha)}$, with high probability on the measurement matrix. In
this paper, we make the observation that the sparsest minimizer subject to
a $\Sigma\Delta$-type quantization constraint would approximate the
original signal from the $\Sigma\Delta$ quantized measurements with a
comparable reconstruction accuracy. Then we show that the less intractable
non-convex $l^\tau$ minimization for $\tau$ sufficiently small can also be
used as an alternative recovery method to achieve a comparable
reconstruction accuracy. In both cases, we remove the requirement that the
quantization alphabet be fine. Finally, we show using these results that
root-exponential accuracy in the bitrate can be achieved for compressed
sensing of sparse signals using $\Sigma\Delta$ quantization as the encoder
and $l^\tau$ minimization as the decoder.}
}
@INPROCEEDINGS{Jacq1307:Quantized,
AUTHOR="Laurent Jacques and K{\'e}vin Degraux and Christophe {De Vleeschouwer}",
TITLE="Quantized Iterative Hard Thresholding: Bridging 1bit and {HighResolution}
Quantized Compressed Sensing",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="105-108",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="quantization, iterative hard thresholding, 1-bit compressed sensing, binary
stable embedding",
ABSTRACT="In this work, we show that reconstructing a sparse signal from quantized
compressive measurement can be achieved in an unified formalism whatever
the (scalar) quantization resolution, i.e., from 1-bit to high resolution
assumption. This is achieved by generalizing the iterative hard
thresholding (IHT) algorithm and its binary variant (BIHT) introduced in
previous works to enforce the consistency of the reconstructed signal with
respect to the quantization model. The performance of this algorithm,
simply called quantized IHT (QIHT), is evaluated in comparison with other
approaches (e.g., IHT, basis pursuit denoise) for several quantization
scenarios."
}
@INPROCEEDINGS{Krah1307:Sigma,
AUTHOR="Felix Krahmer and Rayan Saab and Ozgur Yilmaz",
TITLE="{Sigma-Delta} quantization of sub-Gaussian compressed sensing measurements",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="109-112",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="Recently, it has been shown that for the setup of compressed sensing with
Gaussian measurements that Sigma-Delta quantization can be effectively
incorporated into the sensing mechanism [1]. In contrast to independently
quantized measurements, the resulting schemes yield better reconstruction
accuracy with a higher number of measurements even at a constant number of
bits per signal. The original analysis of this method, however, crucially
depends on the rotation invariance of the Gaussian measurements and hence
does not directly generalize to other classes of measurements. In this
note, we present a refined analysis that allows for a generalization to
arbitrary sub-Gaussian measurements."
}
@INPROCEEDINGS{Fadi1307:Stable,
AUTHOR="Jalal Fadili and Gabriel Peyr{\'e} and Samuel Vaiter and Charles-Alban
Deledalle and Joseph Salmon",
TITLE="Stable Recovery with Analysis Decomposable Priors",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="113-116",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Low complexity models; Decomposable priors; Analysis prior; Recovery
guarantees",
ABSTRACT="In this paper, we investigate in a unified way the structural properties of
solutions to inverse problems. These solutions are regularized by the
generic class of semi-norms defined as a decomposable norm composed with a
linear operator, the so-called analysis type decomposable prior. This
encompasses several well-known analysis-type regularizations such as the
discrete total variation (in any dimension), analysis group-Lasso or the
nuclear norm. Our main results establish sufficient conditions under which
uniqueness and stability to a bounded noise of the regularized solution are
guaranteed. Along the way, we also provide a necessary and sufficient
uniqueness result that is of independent interest and goes beyond the case
of decomposable norms."
}
@INPROCEEDINGS{Cher1307:FRI,
AUTHOR="Tanya Chernyakova and Omer Bar-Ilan and Yonina C. Eldar",
TITLE="{FRI-based} {Sub-Nyquist} Sampling and Beamforming in Ultrasound and Radar",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="117-120",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="FRI; Xampling; beamforming; CS; ultrasound; radar",
ABSTRACT="Signals consisting of short pulses are present in many applications
including ultrawideband communication, object detection and navigation
(radar, sonar) and medical imaging. The structure of such signals,
effectively captured within the finite rate of innovation (FRI) framework,
allows for significant reduction in sampling rates, required for perfect
reconstruction. In this work we consider two applications, ultrasound
imaging and radar, where the FRI signal structure allows to reduce both
sampling and processing rates. Furthermore, we show how the FRI framework
inspires new processing techniques, such as beamforming in the frequency
domain and Doppler focusing. In both applications a pulse of a known shape
or a stream of such pulses is transmitted into the respective medium, and
the received echoes are sampled and digitally processed in a way referred
to as beamforming. Applied either spatially or temporally, beamforming
allows to improve signal-to-noise ratio. In radar applications it also
allows for target Doppler frequency estimation. Using FRI modeling both for
detected and beamformed signals, we are able to reduce sampling rates and
to perform digital beamforming directly on the low-rate samples."
}
@INPROCEEDINGS{Cond1307:Robust,
AUTHOR="Laurent Condat and Akira Hirabayashi",
TITLE="Robust Spike Train Recovery from Noisy Data by Structured Low Rank
Approximation",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="121-124",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Recovery of Dirac pulses; finite rate of innovation; maximum likelihood
estimation; structured low rank approximation; optimization; Cadzow
denoising",
ABSTRACT="We consider the recovery of a finite stream of Dirac pulses at nonuniform
locations, from noisy lowpass-filtered samples. We show that
maximum-likelihood estimation of the unknown parameters amounts to solve a
difficult, even believed NP-hard, matrix problem of structured low rank
approximation. We propose a new heuristic iterative optimization algorithm
to solve it. Although it comes, in absence of convexity, with no
convergence proof, it converges in practice to a local solution, and even
to the global solution of the problem, when the noise level is not too
high. Thus, our method improves upon the classical Cadzow denoising method,
for same implementation ease and speed."
}
@INPROCEEDINGS{Nair1307:Multichannel,
AUTHOR="Amrish Nair and Pina Marziliano and Frank Quick and Ronald Crochiere and
Gilles Baechler",
TITLE="Multichannel {ECG} Analysis using {VPW-FRI}",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="125-128",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Sparse sampling, Multichannel, ECG",
ABSTRACT="In this paper, we present an application of Variable Pulse Width Finite
Rate of Innovation (VPW-FRI) in dealing with multi-channel
Electrocardiogram (ECG) data using a common annihilator. By extending the
conventional FRI model to include additional parameters such as pulse width
and asymmetry, VPW-FRI has been able to deal with a more general class of
pulses. The common annihilator, which is introduced in the annihilating
filter step, shows a common support in multi-channel ECG data, which
provides interesting possibilities in compression. A model based de-noising
method will be presented which is fast and non-iterative. Also, an
application to detect QRS complexes in ECG signals will be demonstrated.
The results will show the robustness of the common annihilator and the QRS
detection even in the presence of noise."
}
@INPROCEEDINGS{Rame1307:Recovery,
AUTHOR="Gayatri Ramesh and Elie Atallah and Qiyu Sun",
TITLE="Recovery of bilevel causal signals with finite rate of innovation using
positive sampling kernels",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="129-132",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="bilevel signal, finite rate of innovation",
ABSTRACT="Bilevel signal $x$ with maximal local rate of innovation $R$ is a
continuous-time signal that takes only two values $0$ and $1$ and that
there is at most one transition position in any time period of $1/R$. In
this note, we introduce a recovery method for bilevel causal signals $x$
with maximal local rate of innovation $R$ from their uniform samples
$x*h(nT), n\ge 1$, where the sampling kernel $h$ is causal and positive on
$(0, T)$, and the sampling rate $\tau:=1/T$ is at (or above) the maximal
local rate of innovation $R$. We also discuss stability of the bilevel
signal recovery procedure in the presence of bounded noises."
}
@INPROCEEDINGS{Urig1307:Approximate,
AUTHOR="Jose Antonio Uriguen and Pier Luigi Dragotti and Thierry Blu",
TITLE="Approximate {FRI} with Arbitrary Kernels",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="133-136",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="FRI, Sampling, Noise, Matrix Pencil, Approximation",
ABSTRACT="In recent years, several methods have been developed for sampling and exact
reconstruction of specific classes of non-bandlimited signals known as
signals with finite rate of innovation (FRI). This is achieved by using
adequate sampling kernels and reconstruction schemes, for example the
exponential reproducing kernels. Proper linear combinations of this type of
kernel with its shifted versions may reproduce polynomials or exponentials
exactly.
In this paper we briefly review the ideal FRI sampling and reconstruction
scheme and some of the existing techniques to combat noise. We then present
an alternative perspective of the FRI retrieval step, based on moments and
approximate reproduction of exponentials. Allowing for a controlled model
mismatch, we propose a unified reconstruction stage that addresses two
current limitations in FRI: the number of degrees of freedom and the
stability of the retrieval. Moreover, the approach is universal in that it
can be used with any sampling kernel from which enough information is
available."
}
@INPROCEEDINGS{Bate1307:Algebraic,
AUTHOR="Dmitry Batenkov and Yosef Yomdin",
TITLE="Algebraic signal sampling, Gibbs phenomenon and Prony-type systems",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="137-140",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Algebraic sampling; Gibbs phenomenon; superresolution; Prony system",
ABSTRACT={Systems of Prony type appear in various reconstruction problems such as
finite rate of innovation, superresolution and Fourier inversion of
piecewise smooth functions. By keeping the number of equations small and
fixed, we demonstrate that such {"}decimation{"} can lead to practical
improvements in the reconstruction accuracy. As an application, we provide
a solution to the so-called Eckhoff's conjecture, which asked for
reconstructing jump positions and magnitudes of a piecewise-smooth function
from its Fourier coefficients with maximal possible asymptotic accuracy --
thus eliminating the Gibbs phenomenon.}
}
@INPROCEEDINGS{Baye1307:(Non,
AUTHOR="Dominik Bayer and Peter Balazs",
TITLE="{(Non-)Density} Properties of Discrete Gabor Multipliers",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="25-28",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Frames; Gabor multipliers",
ABSTRACT="This paper is concerned with the possibility of approximating arbitrary
operators by multipliers for Gabor frames or more general Bessel sequences.
It addresses the question of whether sets of multipliers (whose symbols
come from prescribed function classes such as $\ell^2$) constitute dense
subsets of various spaces of operators (such as Hilbert-Schmidt class). We
prove a number of negative results that show that in the discrete setting
subspaces of multipliers are usually not dense and thus too small to
guarantee arbitrary good approximation. This is in contrast to the
continuous case."
}
@INPROCEEDINGS{Omer1307:Estimation,
AUTHOR="Harold Omer and Bruno {Torr{\'e}sani}",
TITLE="Estimation of frequency modulations on wideband signals; applications to
audio signal analysis",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="29-32",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Time Frequency Analysis, Non Stationary Random Process, Spectral
Estimation, Audio Signal Processing",
ABSTRACT="The problem of joint estimation of power spectrum and modulation from
realizations of frequency modulated stationary wideband signals is
considered. The study is motivated by some specific signal classes from
which departures to stationarity can carry relevant information and has to
be estimated.
The estimation procedure is based upon explicit modeling of the signal as a
wideband stationary Gaussian signal, transformed by time-dependent, smooth
frequency modulation. Under such assumptions, an approximate expression for
the second order statistics of the transformed signal's Gabor transform is
obtained, which leads to an approximate maximum likelihood estimation
procedure.
The proposed approach is validated on numerical simulations."
}
@INPROCEEDINGS{Perr1307:Gabor,
AUTHOR="Nathanaël Perraudin and Nicki Holighaus and Peter Soendergaard and Peter
Balazs",
TITLE="Gabor dual windows using convex optimization",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="33-36",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Time frequency, Gabor analysis, Convex optimization, Dual frames",
ABSTRACT="Redundant Gabor frames admit an infinite number of dual frames, yet only
the canonical dual Gabor system, constructed from the minimal l2-norm dual
window, is widely used. This window function however, might lack desirable
properties, such as good time-frequency concentration, small support or
smoothness. We employ convex optimization methods to design dual windows
satisfying the Wexler-Raz equations and optimizing various constraints.
Numerical experiments show that alternate dual windows with considerably
improved features can be found."
}
@INPROCEEDINGS{Waln1307:Sparse,
AUTHOR="Goetz Pfander and David Walnut",
TITLE="Sparse Finite Gabor Frames for Operator Sampling",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="37-40",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="operator sampling, Gabor frams, Gabor matrices, full Spark frames",
ABSTRACT="We derive some interesting properties of finite Gabor frames and apply them
to the sampling or identification of operators with bandlimited
Kohn-Nirenberg symbols, or equivalently those with compactly supported
spreading functions. Specifically we use the fact that finite Gabor
matrices are full Spark for an open, dense set of window vectors to show
the existence of periodically weighted delta trains that identify
simultaneously large operator classes. We also show that sparse delta
trains exist that identify operator classes for which the spreading support
has small measure."
}
@INPROCEEDINGS{Poon1307:Optimal,
AUTHOR="Clarice Poon and Anders Hansen and Ben Adcock",
TITLE="Optimal wavelet reconstructions from Fourier samples via generalized
sampling",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="41-44",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Sampling theory, Generalized sampling, Wavelets",
ABSTRACT="We consider the problem of computing wavelet coefficients of compactly
supported functions from their Fourier samples. For this, we use the
recently introduced framework of generalized sampling in the context of
compactly supported orthonormal wavelet bases. Our first result
demonstrates that using generalized sampling one obtains a stable and
accurate reconstruction, provided the number of Fourier samples grows
linearly in the number of wavelet coefficients recovered. We also present
the exact constant of proportionality for the class of Daubechies
wavelets.
Our second result concerns the optimality of generalized sampling for this
problem. Under some mild assumptions generalized sampling cannot be
outperformed in terms of approximation quality by more than a constant
factor. Moreover, for the class of so-called perfect methods, any attempt
to lower the sampling ratio below a certain critical threshold necessarily
results in exponential ill-conditioning. Thus generalized sampling provides
a nearly-optimal solution to this problem."
}
@INPROCEEDINGS{Stor1307:Wavelet,
AUTHOR="Martin Storath and Laurent Demaret and Peter Massopust",
TITLE="Wavelet Signs: A New Tool for Signal Analysis",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="45-48",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Wavelet signature; Complex wavelets; Signal analysis; Hilbert transform;
Fractional differentiation and integration; Phase; Sobolev regularity;
Singular support; Salient feature",
ABSTRACT="We propose a new analysis tool for signals, called signature, that is based
on complex wavelet signs. The complex-valued signature of a signal at some
spatial location is defined as the fine-scale limit of the signs of its
complex wavelet coefficients. We show that the signature equals zero at
sufficiently regular points of a signal whereas at salient features, such
as jumps or cusps, it is non-zero. We establish that signature is invariant
under fractional differentiation and rotates in the complex plane under
fractional Hilbert transforms. We derive an appropriate discretization,
which shows that wavelet signatures can be computed explicitly. This allows
an immediate application to signal analysis."
}
@INPROCEEDINGS{Bene1307:Balayage,
AUTHOR="Enrico Au-Yeung and John Benedetto",
TITLE="Balayage and short time Fourier transform frames",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="73-76",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Balayage; spectral synthesis; frames; short time Fourier transform",
ABSTRACT="Using his formulation of the potential theoretic notion of balayage and his
deep results about this idea, Beurling gave sufficient conditions for
Fourier frames in terms of balayage. The analysis makes use of spectral
synthesis, due to Wiener and Beurling, as well as properties of strict
multiplicity, whose origins go back to Riemann. In this setting and with
this technology, we formulate and prove non-uniform sampling formulas in
the context of the short time Fourier transform (STFT)."
}
@INPROCEEDINGS{Mixo1307:Fundamental,
AUTHOR="Afonso Bandeira and Jameson Cahill and Dustin G. Mixon and Aaron Nelson",
TITLE="Fundamental Limits of Phase Retrieval",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="77-80",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="Recent advances in convex optimization have led to new strides in the phase
retrieval problem over finite-dimensional vector spaces. However, certain
fundamental questions remain: What sorts of measurement vectors uniquely
determine every signal up to a global phase factor, and how many are needed
to do so? This paper presents several results that address these questions,
specifically in the less-understood complex case. In particular, we
characterize injectivity, we identify that the complement property is
indeed necessary, we pose a conjecture that 4M-4 generic measurement
vectors are necessary and sufficient for injectivity in M dimensions, and
we describe how to prove this conjecture in the special cases where M=2,3.
To prove the M=3 case, we leverage a new test for injectivity, which can be
used to determine whether any 3-dimensional measurement ensemble is
injective."
}
@INPROCEEDINGS{Chri1307:Transformations,
AUTHOR="Ole Christensen and Say Goh",
TITLE="On transformations between Gabor frames and wavelet frames",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="81-84",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Gabor frames; wavelet frames; dual pairs; exponential B-splines",
ABSTRACT="We describe a procedure that enables us to construct dual pairs of wavelet
frames from certain dual pairs of Gabor frames. Applying the construction
to Gabor frames generated by appropriate exponential B-splines gives
wavelet frames generated by functions whose Fourier transforms are
compactly supported splines with geometrically distributed knot sequences.
There is also a reverse transform, which yields pairs of dual Gabor frames
when applied to certain wavelet frames."
}
@INPROCEEDINGS{Kuty1307:Perfect,
AUTHOR="Gitta Kutyniok and Kasso Okoudjou and Friedrich Philipp",
TITLE="Perfect Preconditioning of Frames by a Diagonal Operator",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="85-88",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="Frames which are tight might be considered optimally conditioned in the
sense of their numerical stability. This leads to the question of perfect
preconditioning of frames, i.e., modification of a given frame to generate
a tight frame. In this paper, we analyze prefect preconditioning of frames
by a diagonal operator. We derive various characterizations of functional
analytic and geometric type of the class of frames which allow such a
perfect preconditioning."
}
@INPROCEEDINGS{Fick1307:Characterizing,
AUTHOR="Matthew Fickus and Miriam Poteet",
TITLE="Characterizing completions of finite frames",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="89-92",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="frame completion; majorization; Schur-Horn",
ABSTRACT={Finite frames are possibly-overcomplete generalizations of orthonormal
bases. We consider the {"}frame completion{"} problem, that is, the problem
of how to add vectors to an existing frame in order to make it better
conditioned. In particular, we discuss a new, complete characterization of
the spectra of the frame operators that arise from those completions whose
newly-added vectors have given prescribed lengths. To do this, we build on
recent work involving a frame's eigensteps, namely the interlacing sequence
of spectra of its partial frame operators. We discuss how such eigensteps
exist if and only if our prescribed lengths are majorized by another
sequence which is obtained by comparing our completed frame's spectrum to
our initial one.}
}
@INPROCEEDINGS{Cahi1307:Note,
AUTHOR="Jameson Cahill and Xuemei Chen",
TITLE="A note on scalable frames",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="93-96",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="frames; scalable",
ABSTRACT="We study the problem of determining whether a given frame is scalable, and
when it is, understanding the set of all possible scalings. We show that
for most frames this is a relatively simple task in that the frame is
either not scalable or is scalable in a unique way, and to find this
scaling we just have to solve a linear system. We also provide some insight
into the set of all scalings when there is not a unique scaling. In
particular, we show that this set is a convex polytope whose vertices
correspond to minimal scalings."
}
@INPROCEEDINGS{Anon1307:Measurement,
AUTHOR="Nathan A Goodman",
TITLE="Measurement Structures and Constraints in Compressive {RF} Systems",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="49-52",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="radar; radar detection; compressive sensing;",
ABSTRACT="Compressive sensing (CS) is a powerful technique for sub-sampling of
signals combined with reconstruction based on sparsity. Many papers have
been published on the topic; however, they often fail to consider practical
hardware factors that may prevent or alter the implementation of desired CS
measurement kernels. In particular, different compressive architectures in
the RF domain either sacrifice collected signal energy or create noise
folding, both of which cause SNR reduction. In this paper, we consider
valid signal models and other system aspects of RF compressive systems."
}
@INPROCEEDINGS{Gehm1307:Calibration—An,
AUTHOR="Michael Gehm",
TITLE="{Calibration—An} open challenge in creating practical computational- and
compressive-sensing systems",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="53-56",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="calibration; computational sensing; compressive sensing",
ABSTRACT="The goal of this manuscript (and associated talk) is not to present any
recent experimental results from my laboratory. Rather, the purpose is to
elucidate why I believe that calibration is one of the few remaining
significant challenges in the struggle to create a wide range of practical
computational sensing and compressive sensing (CS) systems. Toward this
end, I briefly describe the fundamental and implementation difficulties
associated with calibration as well as the existing calibration approaches
and their associated limitations before sketching the theoretical question
that must be addressed in order to solve the calibration challenge."
}
@INPROCEEDINGS{Anit1307:Compressive,
AUTHOR="Laura Anitori and Arian Maleki and Wim {van Rossum} and Matern Otten and
Richard Baraniuk",
TITLE="Compressive {CFAR} Radar Processing",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="57-60",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="In this paper we investigate the performance of a combined Compressive
Sensing (CS) Constant False Alarm Rate (CFAR) radar processor under
different interference scenarios using both the Cell Averaging (CA) and
Order Statistic (OS) CFAR detectors. Using the properties of the Complex
Approximate Message Passing (CAMP) algorithm, we demonstrate that the
behavior of the CFAR processor is independent of the combination with the
non-linear recovery and therefore its performance can be predicted using
standard radar tools. We also compare the performance of the CS CFAR
processor to that of an L1-norm detector using an experimental data set."
}
@INPROCEEDINGS{Krue1307:Sampling,
AUTHOR="Kyle R Krueger and James H McClellan and Waymond R Scott, Jr.",
TITLE="Sampling Techniques for Improved Algorithmic Efficiency in Electromagnetic
Sensing",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="61-64",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="Ground-penetrating radar (GPR) and electromagnetic induction (EMI) sensors
are used to image and detect subterranean objects; for example, in landmine
detection. Compressive sampling at the sensors is important for reducing
the complexity of the acquisition process. However, there is a second form
of sampling done in the imaging-detection algorithms where a parametric
forward model of the EM wavefield is used to invert the measurements. This
parametric model includes all the features that need to be extracted from
the object; for subterranean targets this includes but is not limited to
type, 3D location, and 3D orientation. As parameters are added to the
model, the dimensionality increases. Current sparse recovery algorithms
employ a dictionary created by sampling the entire parameter space of the
model. If uniform sampling is done over the high-dimensional parameter
space, the size of the dictionary and the complexity of the inversion
algorithms grow rapidly, exceeding the capability of real-time processors.
This paper shows that strategic sampling practices can be exploited in both
the parameter space, and the acquisition process to dramatically improve
the efficiency and scalability of the these EM sensor systems."
}
@INPROCEEDINGS{Anon1307:Coding,
AUTHOR="David Brady",
TITLE="Coding and sampling for compressive tomography",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="65-68",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="compressive sampling; computational imaging; tomography",
ABSTRACT="This paper discusses sampling system design for estimation of
multidimensional objects from lower dimensional measurements. We consider
examples in geometric, diffractive, coherence, spectral and temporal
tomography. Compressive tomography reduces or eliminates conventional
tradeoffs between temporal and spatial resolution."
}
@INPROCEEDINGS{Ster1307:Challenges,
AUTHOR="Adrian Stern and Yair Rivenson and Yitzhak August",
TITLE="Challenges in Optical Compressive Imaging and Some Solutions",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="69-72",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="compressed sensing; compressive sensing; compressive imaging; computational
imaging.",
ABSTRACT="The theory of compressive sensing (CS) has opened up new opportunities in
the field of optical imaging. However, its implementation in this field is
often not straight-forward. We list the implementation challenges that
might arise in compressive imaging and present some solutions to overcome
them."
}
@INPROCEEDINGS{Dema1307:Super,
AUTHOR="Laurent Demanet and Deanna Needell and Nam Nguyen",
TITLE="Super-resolution via superset selection and pruning",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="141-144",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Superset method; Shannon-Nyquist; Super-resolution",
ABSTRACT={We present a pursuit-like algorithm that we call the ``superset method{"}
for recovery of sparse vectors from consecutive Fourier measurements in the
super-resolution regime. The algorithm has a subspace identification step
that hinges on the translation invariance of the Fourier transform,
followed by a removal step to estimate the solution's support. The superset
method is always successful in the noiseless regime (unlike $\ell\_1$
minimization) and generalizes to higher dimensions (unlike the matrix
pencil method). Relative robustness to noise is demonstrated numerically.}
}
@INPROCEEDINGS{Fern1307:Support,
AUTHOR="Carlos Fernandez-Granda",
TITLE="Support detection in super-resolution",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="145-148",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="super-resolution, support detection, semidefinite programming, spike
deconvolution, local stability",
ABSTRACT="We study the problem of super-resolving a superposition of point sources
from noisy low-pass data with a cut-off frequency f. Solving a tractable
convex program is shown to locate the elements of the support with high
precision as long as they are separated by 2/f and the noise level is small
with respect to the amplitude of the signal."
}
@INPROCEEDINGS{Need1307:Using,
AUTHOR="Deanna Needell and Atul Divekar",
TITLE="Using Correlated Subset Structure for Compressive Sensing Recovery",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="149-152",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="compressive sensing; superresolution;",
ABSTRACT="Compressive sensing is a methodology for the reconstruction of sparse or
compressible signals using far fewer samples than required by the Nyquist
criterion. However, many of the results in compressive sensing concern
random sampling matrices such as Gaussian and Bernoulli matrices. In common
physically feasible signal acquisition and reconstruction scenarios such as
super-resolution of images, the sensing matrix has a non-random structure
with highly correlated columns. Here we present a compressive sensing
recovery algorithm that exploits this correlation structure. We provide
algorithmic justification as well as empirical comparisons."
}
@INPROCEEDINGS{Shec1307:Sub,
AUTHOR="Yoav Shechtman and Alexander Szameit and Eliahyu Osherovich and Pavel
Sidorenko and Elad Bullkich and Hod Dana and Shy Shoham and Irad Yavneh and
Michael Zibulevsky and Oren Cohen and Yonina C. Eldar and Mordechai Segev",
TITLE="{Sub-Wavelength} Coherent Diffractive Imaging based on Sparsity",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="153-155",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="We propose and experimentally demonstrate a method of performing
single-shot sub-wavelength resolution Coherent Diffractive Imaging (CDI),
i.e. algorithmic object reconstruction from Fourier amplitude measurements.
The method is applicable to objects that are sparse in a known basis. The
prior knowledge of the object's sparsity compensates for the loss of phase
information, and the loss of all information at the high spatial
frequencies occurring in every microscope and imaging system due to the
physics of electromagnetic waves in free-space."
}
@INPROCEEDINGS{Vait1307:Robust,
AUTHOR="Samuel Vaiter and Gabriel Peyr{\'e} and Jalal Fadili",
TITLE="Robust Polyhedral Regularization",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="156-159",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="inverse problem; polyhedral regularization, noise robustness",
ABSTRACT="In this paper, we establish robustness to noise perturbations of polyhedral
regularization of linear inverse problems. We provide a sufficient
condition that ensures that the polyhedral face associated to the true
vector is equal to that of the recovered one. This criterion also implies
that the $\ell^2$ recovery error is proportional to the noise level for a
range of parameter. Our criterion is expressed in terms of the hyperplanes
supporting the faces of the unit polyhedral ball of the regularization.
This generalizes to an arbitrary polyhedral regularization results that are
known to hold for sparse synthesis and analysis $\ell^1$ regularization
which are encompassed in this framework. As a byproduct, we obtain recovery
guarantees for $\ell^\infty$ and $\ell^1-\ell^\infty$ regularization."
}
@INPROCEEDINGS{Cast1307:Performance,
AUTHOR="Rui Castro",
TITLE="On the Performance of Adaptive Sensing for Sparse Signal Inference",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="160-163",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Adaptive Sensing, Compressive Sensing, Detection and Estimation, Sequential
Experimental Design",
ABSTRACT="In this short paper we survey recent results characterizing the fundamental
draws and limitations of adaptive sensing for sparse signal inference. We
consider two different adaptive sensing paradigms, based either on
single-entry or linear measurements. Signal magnitude requirements for
reliable inference are shown for two different inference problems, namely
signal detection and signal support estimation."
}
@INPROCEEDINGS{Char1307:Reconstruction,
AUTHOR="Gilles Chardon and Albert Cohen and Laurent Daudet",
TITLE="Reconstruction of solutions to the Helmholtz equation from punctual
measurements",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="164-167",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="We analyze the sampling of solutions to the Helmholtz equation (e.g. sound
fields in the harmonic regime) using a least-squares method based on
approximations of the solutions by sums of Fourier-Bessel functions or
plane waves. This method compares favorably to others such as Orthogonal
Matching Pursuit with a Fourier dictionary. We show that using a
significant proportion of samples on the border of the domain of interest
improves the stability of the reconstruction, and that using
cross-validation to estimate the model order yields good reconstruction
results."
}
@INPROCEEDINGS{Mula1307:Priori,
AUTHOR="Yvon Maday and Olga Mula and Turinici Gabriel",
TITLE="A priori convergence of the Generalized Empirical Interpolation Method",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="168-171",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="empirical, interpolation, reduced basis, convergence, decay rates",
ABSTRACT="In an effort to extend the classical lagrangian interpolation tools, new
interpolating methods that use general interpolating functions are
explored. The Generalized Empirical Interpolation Method (GEIM) belongs to
this class of new techniques. It generalizes the plain Empirical
Interpolation Method by replacing the evaluation at interpolating points by
application of a class of interpolating linear functions. Since its
efficiency depends critically on the choice of the interpolating functions
(that are chosen by a Greedy selection procedure), the purpose of this
paper is therefore to provide a priori convergence rates for the Greedy
algorithm that is used to build the GEIM interpolating spaces."
}
@INPROCEEDINGS{Vats1307:Test,
AUTHOR="Divyanshu Vats and Christoph Studer and Richard Baraniuk",
TITLE="Test-size Reduction Using Sparse Factor Analysis",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="172-175",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="personalized learning; subset selection ; sensor selection ;",
ABSTRACT="Consider a large database of questions that test the knowledge of learners
(e.g., students) about a range of different concepts. While the main goal
of personalized learning is to obtain accurate estimates of each learner's
concept understanding, it is additionally desirable to reduce the number of
questions to minimize each learner's workload. In this paper, we propose a
novel method to extract a small subset of questions (from a large question
database) that still enables the accurate estimation of a learner's concept
understanding. Our method builds upon the SPARse Factor Analysis (SPARFA)
framework and chooses a subset of questions that minimizes the entropy of
the error in estimating the level of concept understanding. We approximate
the underlying combinatorial optimization problem using a mixture of convex
and greedy methods and demonstrate the efficacy of our approach on real
educational data."
}
@INPROCEEDINGS{Abre1307:Special,
AUTHOR="Daniel Abreu",
TITLE="Special Frames",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="176-177",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Frames, special functions, Gabor frames, wavelet frames",
ABSTRACT="We will present three classes of special frames: special Fourier-type
frames, special Gabor frames and special wavelet frames. Then we will give
one example for each class: Fourier-Bessel frames, Gabor frames with
Hermite functions and wavelet frames with Laguerre functions. Some results
about these three class of special frames, currently under investigation,
will be outlined."
}
@INPROCEEDINGS{Ange1307:Variation,
AUTHOR="Laura Angeloni and Gianluca Vinti",
TITLE="Variation and approximation for Mellin-type operators",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="178-181",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Variation; Mellin operators; convergence; rate of approximation",
ABSTRACT="Mellin analysis is of extreme importance in approximation theory, also for
its wide applications: among them, for example, it is connected with
problems of Signal Analysis, such as the Exponential Sampling. Here we
study a family of Mellin-type integral operators defined as $$ (T\_w
f)({\tt s})=\int\_{\R\_+^N} K\_w({\tt t}) f({\tt st}){\,d{\tt t} \over
\langle{\tt t}\rangle}, \ {\tt s}\in \R\_+^N,\ w>0,\eqno \rm{(I)} $$ where
$\{K\_w\}\_{w>0}$ are approximate identities, $\langle{\tt
t}\rangle:=\prod\_{i=1}^N t\_i,$ ${\tt t}=(t\_1,\dots,t\_N)\in \R^N\_+$,
and $f:\R\_+^N\rightarrow \R$ is a function of bounded $\varphi-$variation.
We use a new concept of multidimensional $\varphi-$variation inspired by
the Tonelli approach, which preserves some of the main properties of the
classical variation. For the family of operators (I), besides several
estimates and a result of approximation for the $\varphi-$modulus of
smoothness, the main convergence result that we obtain proves that $$
\lim\_{w\to +\infty} V^{\varphi}[\lambda(T\_w f-f)]=0, $$ for some
$\lambda>0$, provided that $f$ is $\varphi-$absolutely continuous.
Moreover, the problem of the rate of approximation is studied, taking also
into consideration the particular case of Fej\'er-type kernels."
}
@INPROCEEDINGS{Azgh1307:Iterative,
AUTHOR="Masomeh Azghani and Farokh Marvasti",
TITLE="iterative methods for random sampling recovery and compressed sensing
recovery",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="182-185",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="In this paper, an iterative sparse recovery method based on sampling and
interpolation is suggested. The proposed method exploits the sparsity of
the embedded signal to recover it from random samples. Simulation results
indicate that the proposed method outperforms IMAT (a random sampling
recovery method) and OMP (compressed sensing recovery method) in the case
of image compression. Also an iterative method with adaptive thresholding
for compressed sensing (IMATCS) recovery is proposed. Unlike its similar
counterpart, iterative hard thresholding (IHT), the thresholding function
of the proposed method is adaptive i.e. the threshold value changes with
the iteration number, which enables IMATCS to reconstruct the sparse signal
without having any knowledge of the sparsity number. The simulation results
indicate that IMATCS outperforms IHT in both computational complexity and
quality of the recovered signal. Compared to the orthogonal matching
pursuit (OMP), the proposed method is computationally more efficient with
similar recovery performance."
}
@INPROCEEDINGS{Bala1307:Review,
AUTHOR="Peter Balazs and Diana Stoeva",
TITLE="A Review of the Invertibility of Frame Multipliers",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="186-188",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Multiplier; Invertibility; Frame; Riesz basis; Bessel sequence",
ABSTRACT="In this paper we give a review of recent results on the invertibility of
frame multipliers $M\_{m,\Phi,\Psi}$. In particular we give sufficient,
necessary or equivalent conditions for the invertibility of such operators,
depending on the properties of the sequences $\Psi$, $\Phi$ and $m$. We
consider Bessel sequences, frames and Riesz sequences."
}
@INPROCEEDINGS{Bart1307:Hybrid,
AUTHOR="Andreas Bartels",
TITLE="Hybrid Regularization and Sparse Reconstruction of Imaging Mass
Spectrometry Data",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="189-192",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="Imaging mass spectrometry (IMS) is a technique to visualize the molecular
distributions from biological samples without the need of chemical labels
or antibodies. The underlying data is taken from a mass spectrometer that
ionizes the sample on spots on a grid of a certain size. Mathematical
postprocessing methods has been investigated twice for better visualization
but also for reducing the huge amount of data. We propose a first model
that applies compressed sensing to reduce the number of measurements needed
in IMS. At the same time we apply peak picking in spectra using the l1-norm
and denoising on the m/z-images via the TV-norm which are both general
procedures of mass spectrometry data postprocessing, but always done
separately and not simultaneous. This is realized by using a hybrid
regularization approach for a sparse reconstruction of both the spectra and
the images. We show reconstruction results for a given rat brain dataset in
spectral and spatial domain."
}
@INPROCEEDINGS{Bide1307:Level,
AUTHOR="Brigitte Bidegaray-Fesquet and Marianne Clausel",
TITLE="Level crossing sampling of strongly monoH{\"o}lder functions",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="193-196",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="non uniform sampling; monoH{\"o}lderian function",
ABSTRACT="We address the problem of quantifying the number of samples that can be
obtained through a level crossing sampling procedure for applications to
mobile systems. We specially investigate the link between the smoothness
properties of the signal and the number of samples, both from a theoretical
and a numerical point of view."
}
@INPROCEEDINGS{Bost1307:MAP,
AUTHOR="Emrah Bostan and Julien Fageot and Ulugbek S. Kamilov and Michael Unser",
TITLE="{MAP} Estimators for {Self-Similar} Sparse Stochastic Models",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="197-199",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Innovation models; fractional Laplacian; fractals; invariance;
self-similarity; sparse stochastic processes; MAP estimation",
ABSTRACT="We consider the reconstruction of multi-dimensional signals from noisy
samples. The problem is formulated within the framework of the theory of
continuous-domain sparse stochastic processes. In particular, we study the
fractional Laplacian as the whitening operator specifying the correlation
structure of the model. We then derive a class of MAP estimators where the
priors are confined to the family of infinitely divisible distributions.
Finally, we provide simulations where the derived estimators are compared
against total-variation (TV) denoising."
}
@INPROCEEDINGS{Chau1307:Variable,
AUTHOR="Nicolas Chauffert and Philippe Ciuciu and Pierre Armand Weiss and Fabrice
Gamboa",
TITLE="From variable density sampling to continuous sampling using Markov chains",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="200-203",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Compressed Sensing | Markov chains | variable density random undersampling
| MRI",
ABSTRACT="Since its discovery over the last decade, Compressed Sensing (CS) has been
successfully applied to Magnetic Resonance Imaging (MRI). It has been shown
to be a powerful way to reduce scanning time without sacrificing image
quality. MR images are actually strongly compressible in a wavelet basis,
the latter being largely incoherent with the k-space or spatial Fourier
domain where acquisition is performed. Nevertheless, since its first
application to MRI [1], the theoretical justification of actual k-space
sampling strategies is questionable. Indeed, the vast majority of k-space
sampling distributions have been heuristically designed (e.g., variable
density) or driven by experimental feasibility considerations (e.g., random
radial or spiral sampling to achieve smoothness k-space trajectory). In
this paper, we try to reconcile very recent CS results with the MRI
specificities (magnetic field gradients) by enforcing the measurements,
i.e. samples of k-space, to fit continuous trajectories. To this end, we
propose random walk continuous sampling based on Markov chains and we
compare the reconstruction quality of this scheme to the state-of-the art."
}
@INPROCEEDINGS{Conn1307:Comparison,
AUTHOR="Nicholas Conn and David Borkholder",
TITLE="A Comparison of Reconstruction Methods for Compressed Sensing of the
Photoplethysmogram",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="204-207",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Compressed Sensing, Compressive Sensing, LASSO, Penalty Parameter,
Optimization, Photoplethysmogram, Sparsity, Reconstruction",
ABSTRACT="Compressed sensing has the possibility to significantly decrease the power
consumption of wireless medical devices. The photoplethysmogram (PPG) is a
device which can greatly benefit from compressed sensing due to the large
amount of power needed to capture data. The aim of this paper is to
determine if the least absolute shrinkage and selection operator (LASSO)
optimization algorithm is the best approach for reconstructing a
compressively sampled PPG across varying physiological states. The results
show that LASSO reconstruction approaches, but does not surpass, the
reliability of constrained optimization."
}
@INPROCEEDINGS{Fern1307:Generalized,
AUTHOR="H{\'e}ctor {Fern{\'a}ndez-Morales} and Antonio {García} and Miguel
{Hern{\'a}ndez-Medina}",
TITLE="Generalized sampling in $U$-invariant subspaces",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="208-211",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="$U$-invariant subspaces; generalized sampling; frame; time jitter error",
ABSTRACT="In this work we carry out some results in sampling theory for $U$-invariant
subspaces of a separable Hilbert space $\mathcal{H}$, also called atomic
subspaces: \[ \mathcal{A}\_a=\big\{\sum\_{n\in\mathbb{Z}}a\_nU^na:\,
\{a\_n\} \in \ell^2(\mathbb{Z}) \big\}\,, \] where $U$ is an unitary
operator on $\mathcal{H}$ and $a$ is a fixed vector in $\mathcal{H}$. These
spaces are a generalization of the well-known shift-invariant subspaces in
$L^2(\mathbb{R})$; here the space $L^2(\mathbb{R})$ is replaced by
$\mathcal{H}$, and the shift operator by $U$. Having as data the samples of
some related operators, we derive frame expansions allowing the recovery of
the elements in $\mathcal{A}\_a$. Moreover, we include a frame
perturbation-type result whenever the samples are affected with a jitter
error."
}
@INPROCEEDINGS{Giry1307:Iterative,
AUTHOR="Raja Giryes and Michael Elad",
TITLE="Iterative Hard Thresholding with Near Optimal Projection for Signal
Recovery",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="212-215",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Iterative Hard Thresholding, D-RIP, Sparse Representation, Compressed
Sensing, Coherent Dictionaries",
ABSTRACT="Recovering signals that have sparse representations under a given
dictionary from a set of linear measurements got much attention in the
recent decade. However, most of the work has focused on recovering the
signal's representation, forcing the dictionary to be incoherent and with
no linear dependencies between small sets of its columns. A series of
recent papers show that such dependencies can be allowed by aiming at
recovering the signal itself. However, most of these contributions focus on
the analysis framework. One exception to these is the work reported in
[Davenport, Needell and Wakin, 2012], proposing a variant of the CoSaMP for
the synthesis model, and showing that signal recovery is possible even in
high-coherence cases. In the theoretical study of this technique the
existence of an efficient near optimal projection scheme is assumed. In
this paper we extend the above work, showing that under very similar
assumptions, a variant of IHT can recover the signal in cases where regular
IHT fails."
}
@INPROCEEDINGS{Hur1307:Non,
AUTHOR="Youngmi Hur and Fang Zheng",
TITLE="The Design of Non-redundant Directional Wavelet Filter Bank Using {1-D}
Neville Filters",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="216-219",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="In this paper, we develop a method to construct non-redundant directional
wavelet filter banks. Our method uses a special class of filters called
Neville filters and can construct non-redundant wavelet filter banks in any
dimension for any dilation matrix. The resulting filter banks have
directional analysis highpass filters, thus can be used in extracting
directional contents in multi-D signals such as images. Furthermore, one
can custom-design the directions of highpass filters in the filter banks."
}
@INPROCEEDINGS{Kama1307:Sparse,
AUTHOR="Masaru Kamada and Masakazu Ohno",
TITLE="Sparse Approximation of {Ion-Mobility} Spectrometry Profiles by Minutely
Shifted Discrete B-splines",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="220-223",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="splines; sparse approximation; spectrometry",
ABSTRACT="Employing discrete B-splines instead of the Gaussian distribution, we
construct an algorithm for the analysis of ion-mobility spectrometry
profiles. The algorithm is suitable for hardware implementation because the
discrete B-splines are supported by a simple digital filter to compute
their weighted sum and their correlations with a given signal. Minutely
shifted discrete B-splines are deployed of which weighted sum is to
approximate a given profile with non-negative weights. Closely neighboring
discrete B-splines are almost linearly dependent so that they may cause
numerical instability in the approximation process. But numerical
experiments deny this anxiety at least for the final results. Varying the
width of discrete B-splines, we obtain a number of different
approximations. Out of sufficiently precise approximations, we choose the
sparsest one in the sense that it comprises few discrete B-splines with
large weights."
}
@INPROCEEDINGS{Kars1307:Tracking,
AUTHOR="Evripidis Karseras and Kin K. K. Leung and Wei Dai",
TITLE="Tracking Dynamic Sparse Signals with Kalman Filters: Framework and Improved
Inference",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="224-227",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="HIerarchical, Kalman, filter, sparse, dynamic, Bayesian",
ABSTRACT="The standard Kalman filter performs optimally for conventional signals but
tends to fail when it comes to recovering dynamic sparse signals. In this
paper a method to solve this problem is proposed. The basic idea is to
model the system dynamics with a hierarchical Bayesian network which
successfully captures the inherent sparsity of the data, in contrast to the
traditional state-space model. This probabilistic model provides all the
necessary statistical information needed to perform sparsity-aware
predictions and updates in the Kalman filter steps. A set of theorems show
that a properly scaled version of the associated cost function can lead to
less greedy optimisation algorithms, unlike the ones previously proposed.
It is demonstrated empirically that the proposed method outperforms the
traditional Kalman filter for dynamic sparse signals and also how the
redesigned inference algorithm, termed here Bayesian Subspace Pursuit (BSP)
greatly improves the inference procedure."
}
@INPROCEEDINGS{Kivi1307:Variation,
AUTHOR={Andi Kivinukk and Tarmo {Metsm{\"a}gi}},
TITLE="The Variation Detracting Property of some Shannon Sampling Series and their
Derivatives",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="228-231",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="In this paper are considered some generalized Shannon sampling operators
which preserve the total variation of functions and their derivatives. For
that purpose will be used the averaged kernel functions of certain even
band-limited kernel functions."
}
@INPROCEEDINGS{Kont1307:Jointly,
AUTHOR="Apostolos Kontakis and Xander Campman and Geert Leus and Zijian Tang and
Mike Danilouchkine",
TITLE="Jointly filtering and regularizing seismic data using space-varying {FIR}
filters",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="232-235",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="Array forming in seismic data acquisition can be likened to FIR filtering.
Misplacement of the receivers used to record seismic waves can lead to
degraded performance with respect to the filtering characteristics of the
array. We propose two methods for generating linear space-varying filters
that take receiver misplacements into account and demonstrate their
performance on synthetic data."
}
@INPROCEEDINGS{LePe1307:Non,
AUTHOR="Tugdual {Le Pelleter} and Taha Beyrouthy and Robin Rolland and Agn{\`e}s
Bonvilain and Laurent Fesquet",
TITLE="Non-uniform sampling pattern recognition based on atomic decomposition",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="236-239",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="non-uniform sampling;asynchronous;pattern recognition;low-power",
ABSTRACT="Non-uniform sampling is an interesting scheme that can outperforms the
uniform sampling with low activity signals. With such signals, it generates
fewer samples, which means less data to process and lower power
consumption. In addition, it is well-known that asynchronous logic is a low
power technology. This paper deals with the coupling between a non-uniform
sampling scheme and a pattern recognition algorithm implemented with an
event-driven logic. This non-uniform analog-to-digital conversion and the
specific processing have been implemented on an Altera FPGA platform. This
paper reports the first results of this low-activity pattern recognition
system and its availability to recognize specific patterns with very few
samples. The objectives of this work target the future ultra-low power
integrated systems."
}
@INPROCEEDINGS{Shmu1307:Particle,
AUTHOR="Yaniv Shmueli and Gil Shabat and Amit Bermanis and Amir Averbuch",
TITLE="Particle Filter Acceleration Using Multiscale Sampling Methods",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="240-243",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="particle filter, multiscale methods, nonlinear tracking",
ABSTRACT="We present a multiscale based method that accelerates the computation of
particle filters. Particle filter is a powerful method that tracks the
state of a target based on non-linear observations. Unlike the conventional
way that calculates weights over all particles in each cycle of the
algorithm, we sample a small subset from the source particles using matrix
decomposition methods. Then, we apply a function extension algorithm that
uses the particle subset to recover the density function for all the rest
of the particles. As often happens, the computational effort is substantial
especially when tracking multiple objects takes place. The proposed
algorithm reduces significantly the computational load. We demonstrate our
method on both simulated and on real data such as tracking in videos
sequences."
}
@INPROCEEDINGS{Ye1307:Analysis,
AUTHOR="Zhengmao Ye and Habib Mohamadian",
TITLE="Analysis of Multistage Sampling Rate Conversion for Potential Optimal
Factorization",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="244-247",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Polyphase FIR Filter, Interpolation, Decimation, Sampling Rate Conversion,
Multistage, Multirate, Optimization",
ABSTRACT="Digital multistage sampling rate conversion has many engineering
applications in fields of signal and image processing, which is to adapt
the sampling rates to the flows of diverse audio and video signals. The FIR
(Finite Impulse Response) polyphase sampling rate converter is one of
typical schemes that are suitable for interpolation or decimation by an
integer factor. It also guarantees the stability performance with the
stable gain margin and phase margin. The big challenge occurs upon
implementation when a very high order filter is needed with large values of
L (positive integer factor of interpolator) and/or M (positive integer
factor of decimator). Narrowband linear phase filter specifications are
hard to achieve, however. It leads to extra storage space, additional
computation expense and detrimental finite word length effects. The
multistage sampling rate converter has been introduced to factorize the L
and M ratio into a product of ratios of integers or prime numbers. The
optimal number of stages and optimal converting factors are both critical
terms to minimize the computation time and storage requirements. Filter
structure analysis is conducted in this study to search for the potential
factors that could have a remarkable impact to optimize the sampling rate
conversion."
}
@INPROCEEDINGS{Rauh1307:Sparse,
AUTHOR="Andre Rauh and Gonzalo Arce",
TITLE="Sparse {2D} Fast Fourier Transform",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="248-251",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="FFT, sparse, signal processing, 2D, sFFT",
ABSTRACT="This paper extends the concepts of the Sparse Fast Fourier Transform (sFFT)
Algorithm to work with two dimensional (2D) data. The 2D algorithm requires
several generalizations to multiple key concepts of the 1D sparse Fourier
transform algorithm. Furthermore, several parameters needed in the
algorithm are optimized for the reconstruction of sparse image spectra.
This paper addresses the case of the exact k-sparse Fourier transform but
the underlying concepts can be applied to the general case of finding a
k-sparse approximation of the Fourier transform of an arbitrary signal. The
proposed algorithm can further be extended to even higher dimensions.
Simulations illustrate the efficiency and accuracy of the proposed
algorithm when applied to real images."
}
@INPROCEEDINGS{Shec1307:GESPAR,
AUTHOR="Yoav Shechtman and Amir Beck and Yonina C. Eldar",
TITLE="{GESPAR:} Efficient Sparse Phase Retrieval with Application to Optics",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="252-255",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="The problem of phase retrieval, namely, recovery of a signal from the
magnitude of its Fourier transform is ill-posed since the Fourier phase
information is lost. Therefore, prior information on the signal is needed
in order to recover it. In this work we consider the case in which the
prior information on the signal is that it is sparse, i.e., it consists of
a small number of nonzero elements. We propose GESPAR: A fast local search
method for recovering a sparse signal from measurements of its Fourier
transform magnitude. Our algorithm does not require matrix lifting, unlike
previous approaches, and therefore is potentially suitable for large scale
problems such as images. Simulation results indicate that the proposed
algorithm is fast and more accurate than existing techniques. We
demonstrate applications in optics where GESPAR is generalized and used for
finding sparse solutions to sets of quadratic measurements."
}
@INPROCEEDINGS{Bouf1307:Sparse,
AUTHOR="Petros T Boufounos",
TITLE="Sparse Signal Reconstruction from Phase-only Measurements",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="256-259",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="randomized embeddings; phase measurements; compressive sensing;",
ABSTRACT="We demonstrate that the phase of complex linear measurements of signals
preserves significant information about the angles between those signals.
We provide stable angle embedding guarantees, akin to the restricted
isometry property in classical compressive sensing, that characterize how
well the angle information is preserved. They also suggest that a number of
measurements linear in the sparsity and logarithmic in the dimensionality
of the signal contains sufficient information to acquire and reconstruct a
sparse signal within a positive scalar factor. We further show that the
reconstruction can be formulated and solved using standard convex and
greedy algorithms taken directly from the CS literature. Even though the
theoretical results only provide approximate reconstruction guarantees, our
experiments suggest that exact reconstruction is possible."
}
@INPROCEEDINGS{Fate1307:Optimal,
AUTHOR="Mitra Fatemi and Loic Baboulaz and Martin Vetterli",
TITLE="Optimal Sampling Rates in {Infinite-Dimensional} Compressed Sensing",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="260-263",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Generalized sampling, infinite-dimensional compressed sensing, random
sampling, sampling rate",
ABSTRACT="The theory of compressed sensing studies the problem of recovering a high
dimensional sparse vector from its projections onto lower dimensional
subspaces. The recently introduced framework of infinite-dimensional
compressed sensing [1], to some extent generalizes these results to
infinite-dimensional scenarios. In particular, it is shown that the
continuous-time signals that have sparse representations in a known domain
can be recovered from random samples in a different domain. The range M and
the minimum number m of samples for perfect recovery are limited by a
balancing property of the two bases. In this paper, by considering Fourier
and Haar wavelet bases, we experimentally show that M can be optimally
tuned to minimize the number of samples m that guarantee perfect recovery.
This study does not have any parallel in the finite-dimensional CS."
}
@INPROCEEDINGS{Gan1307:Deterministic,
AUTHOR="Lu Gan and Wang Huali",
TITLE="Deterministic Binary Sequences for Modulated Wideband Converter",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="264-267",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="The modulated wideband converter (MWC) is a promising spectrum blind,
sub-Nyquist multi-channel sampling scheme for sparse multi-band signals. In
an MWC, the input analog signal is modulated by a bank of periodic binary
waveforms, low-pass filtered and then down sampled uniformly at a low rate.
One important issue in the design and implementation of an MWC system is
the selection of binary waveforms, which impacts the stability of sparse
reconstruction. In this paper, we propose to construct the binary pattern
with a circulant structure, in which each row is a random cyclic shift of a
single deterministic sequence or a pair of complementary sequences. Such
operators have hardware friendly structures and fast computation in
recovery. They are incoherent with the FFT matrix and the corresponding
sampling operators satisfy the restricted isometry property with
sub-optimal bounds. Some simulation results are included to demonstrate the
validity of the proposed sampling operators."
}
@INPROCEEDINGS{Zaye1307:Fractional,
AUTHOR="Ahmed Zayed",
TITLE="Fractional Prolate Spheroidal Wave Functions",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="268-270",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Fractional Fourier transform, Energy concentration, Prolate spheroidal wave
functions,",
ABSTRACT="An important problem in communication engineering is the energy
concentration problem, that is the problem of finding a signal bandlimited
to $[-\sigma, \sigma]$ with maximum energy concentration in the interval
$[-\tau, \tau], 0<\tau ,$ in the time domain or equivalently, finding a
signal that is time limited to the interval $[-\tau, \tau]$ with maximum
energy concentration in $[-\sigma, \sigma]$ in the frequency domain. This
problem was solved by a group of mathematicians at Bell Labs in the early
1960's. The solution involves the prolate spheroidal wave functions which
are eigenfunctions of a differential and an integral equations.
The main goal of this talk is to solve the energy concentration problem in
the fractional Fourier transform domain, that is to find a signal that is
bandlimited to $[-\sigma, \sigma]$ in the fractional Fourier transform
domain with maximum energy concentration in the interval $[-\tau, \tau],
0<\tau ,$ in the time domain. The solution involves a generalization of the
prolate spheroidal wave functions which we call fractional prolate
spheroidal wave functions. \end{abstract}"
}
@INPROCEEDINGS{Golu1307:Absolute,
AUTHOR="Boris Golubov and Sergey Volosivets",
TITLE="Absolute Convergence of the Series of {Fourier-Haar} Coefficients",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="271-273",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="We give some sharp statements on absolute convergence of the series of
Fourier-Haar coefficients. There are two-dimensional analogs of
one-dimensional results."
}
@INPROCEEDINGS{Butz1307:Mellin,
AUTHOR="Paul Butzer and Carlo Bardaro and Ilaria Mantellini",
TITLE="Mellin analysis and exponential sampling. Part {I:} Mellin fractional
integrals",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="274-276",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Hadamard- type fractional integrals; Mellin transform; semigroup property",
ABSTRACT="The Mellin transform and the associated convolution integrals are
intimately connected with the exponential sampling theorem. Thus it is very
important to develop the various tools of Mellin analysis. In this part we
pave the way to sampling analysis by studying basic theoretical properties,
including Mellin-type fractional integrals, and give a new approach and
version on these integrals, specifying their basic semigroup property.
Especially their domain and range need be studied in detail."
}
@INPROCEEDINGS{Bard1307:Mellin,
AUTHOR="Paul Butzer and Carlo Bardaro and Ilaria Mantellini",
TITLE="Mellin analysis and exponential sampling. Part {II:} Mellin differential
operators and sampling",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="277-280",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="strong and pointwise fractional derivatives; Mellin transform; exponential
sampling; reproducing kernel formula; Mellin-Poisson summation formula",
ABSTRACT="Here, we introduce a notion of strong fractional derivative and we study
the connection with the pointwise fractional derivative, which is defined
by means of Hadamard-type integrals. The main result is a fractional
version of the fundamental theorem of integral and differential calculus in
Mellin frame. Finally there follow the first of several theorems in the
sampling area, the highlight being the reproducing kernel theorem as well
as its approximate version for non-bandlimited functions in the Mellin
sense, both being new."
}
@INPROCEEDINGS{Heil1307:Super,
AUTHOR="Mike Heilemann",
TITLE="From super-resolution microscopy towards quantitative single-molecule
biology",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="281-280",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="In the fluorescence microscopy field, much interest has focused on new
super-resolution techniques (collectively known as PALM/STORM, STED, SIM
and others) [1] that have demonstrated to bypass the diffraction limit and
provide a spatial resolution reaching a near-molecular level. With these
techniques, it has become possible to image cellular structures in far
greater detail than ever before. Single-molecule based methods such as
photoactivation-localization microscopy (PALM) [1], stochastic optical
reconstruction microscopy (STORM) [2] and directSTORM (dSTORM) [3] employ
photoswitchable fluorophores and single-molecule localization to generate a
super-resolution image. These methods are uniquely suited not only to
resolve small cellular structures, but also to provide quantitative
information on the number of molecules or stoichiometries. This talk will
summarize our recent efforts in single-molecule based super-resolution
imaging. It will include experimental developments, such as 3D tissue
imaging [4] and new labeling strategies for cellular structures [5].
Furthermore, single-molecule based super-resolution methods are uniquely
suited not only to resolve small cellular structures, but also to quantify
these by extracting the number of molecules or stoichiometries [6]."
}
@INPROCEEDINGS{Hold1307:Optimisation,
AUTHOR="Seamus Holden and Thomas Pengo and Suliana Manley",
TITLE="Optimisation and control of sampling rate in localisation microscopy",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="281-284",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Localisation microscopy; image analysis; high-density fitting; automation;
closed-loop;",
ABSTRACT={Localisation microscopy (PALM/ STORM, etc.) involves sampling sparse
subsets of fluorescently labelled molecules, so that the density of bright
({"}active{"}) molecules in a single frame is low enough to allow single
molecule sub-diffraction limited localisation. The sampling rate, ie. the
mean number of active molecules per unit time, is controlled by the
illumination intensity of a {"}photoactivation{"} UV laser. Two key
sampling problems are inherent in any localisation microscopy measurement:
1. What is the maximum sampling rate before sub-diffraction limited
resolution is lost? The maximum sampling rate determines the temporal
resolution of the technique. Clearly, the absolute maximum sampling rate is
for all molecules to be active (conventional microscopy). However, the
maximum usable sampling rate is largely determined by the localisation
algorithm used. Our algorithm, DAOSTORM, is a high-density localisation
algorithm which allows an order of magnitude increase in sampling rate
compared to traditional low-density algorithms.
2. Can we automatically maintain optimal sampling rate during data
acquisition? A careful balance in sampling rate is required: if sampling
rate is too high, spatial resolution is reduced; if sampling rate is too
low, temporal resolution is reduced. Traditionally, sampling rate is
controlled by continuous manual assessment of the density of molecules in
any single frame, and manual adjustment of photoactivation laser intensity.
This is tedious, and incompatible with automation. To resolve this, we
present AutoLase, an algorithm for real-time closed-loop measurement and
control of sampling rate.}
}
@INPROCEEDINGS{Huan1307:STORM,
AUTHOR="Bo Huang and Lei Zhu and Joerg Schnitzbauer",
TITLE="{STORM} by compressed sensing",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="285-284",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Super resolution microscopy, compressed sensing",
ABSTRACT="In super-resolution microscopy methods based on single-molecule switching,
each camera snapshot samples a random, sparse subset of probe molecules in
the samples. The final super-resolution image is assembled from thousands
of such snapshots. The rate of accumulating single-molecule activation
events often limits the time resolution. We have developed a sparse-signal
recovery technique using compressed sensing to analyze camera images with
highly overlapping fluorescent spots. This method allows an activated
fluorophore density an order of magnitude higher than what conventional
single-molecule fitting methods can handle. Combination of compressed
sensing with Bayesian statistics over the entire image sequence further
enabled us to improve the spatial precision of determining fluorescent
probe positions."
}
@INPROCEEDINGS{LeMo1307:Video,
AUTHOR="Yoann Le-Montagner and Elsa Angelini and Jean-Christophe Olivo-Marin",
TITLE="Video sampling and reconstruction using linear or non-linear Fourier
measurements",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="285-284",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="The theory of compressed sensing (CS) predicts that structured images can
be sampled in a compressive manner with very few non-adaptive linear
measurements, made in a proper adjacent domain. However, is such a recovery
still possible with nonlinear measurements, such as optical-based Fourier
modulus? Here, we investigate how phase retrieval methods can be extended
to solve the problem of recovering a video signal from a subset of Fourier
modulus samples, taking advantage of some relevant sparse prior assumptions
on the signal of interest. We compare this recovery technique to the usual
convex reconstruction method encountered when dealing with linear CS
measurements. We present some simulation results obtained on real video
sequences coming from biological imaging experiment."
}
@INPROCEEDINGS{Kim1307:Fast,
AUTHOR="Kyung Sang Kim and Junhong Min and Lina Carlini and Michael Unser and
Suliana Manley and Daejong Jeon and Jong Chul Ye",
TITLE="Fast Maximum Likelihood High-density {Low-SNR} Super-resolution
Localization Microscopy",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="285-288",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="Localization microscopy such as STORM/PALM achieves the super-resolution by
sparsely activating photo-switchable probes. However, to make the
activation sparse enough to obtain reconstruction images using conventional
algorithms, only small set of probes need to be activated simultaneously,
which limits the temporal resolution. Hence, to improve temporal resolution
up to a level of live cell imaging, high-density imaging algorithms that
can resolve several overlapping PSFs are required. In this paper, we
propose a maximum likelihood algorithm under Poisson noise model for the
high-density low-SNR STORM/PALM imaging. Using a sparsity promoting prior
with concave-convex procedure (CCCP) optimization algorithm, we achieved
high performance reconstructions with ultra-fast reconstruction speed of 5
second per frame under high density low SNR imaging conditions.
Experimental results using simulated and real live-cell imaging data
demonstrate that proposed algorithm is more robust than conventional
methods in terms of both localization accuracy and molecular recall rate."
}
@INPROCEEDINGS{Heis1307:Analogies,
AUTHOR="Bettina Heise and Stefan Schausberger and Martin Reinhardt and David
Stifter",
TITLE="Analogies and differences in optical and mathematical systems and
approaches",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="289-292",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="programmable optics, Fourier filter, image transforms, contrast, optical
imaging",
ABSTRACT="We review traditions and trends in optics and imaging recently arising by
applying programmable optical devices and by sophisticated approaches for
data evaluation and image reconstruction. Furthermore, a short overview is
given about modeling of well-known classical optical elements, and vice
versa, about optical realizations of classical mathematical transforms, as
in particular Fourier, Hilbert, and Riesz transforms."
}
@INPROCEEDINGS{Robi1307:Nyquist,
AUTHOR="Michael Robinson",
TITLE="The Nyquist theorem for cellular sheaves",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="293-296",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="sheaf; ambiguity; cohomology; nyquist theorem",
ABSTRACT="We develop a unified sampling theory based on sheaves and show that the
Shannon-Nyquist theorem is a cohomological consequence of an exact sequence
of sheaves. Our theory indicates that there are additional cohomological
obstructions for higher-dimensional sampling problems. Using these
obstructions, we also present conditions for perfect reconstruction of
piecewise linear functions on graphs, a collection of non-bandlimited
functions on topologically nontrivial domains."
}
@INPROCEEDINGS{Rome1307:Frames,
AUTHOR="Jos{\'e} Luis Romero and Monika Doerfler",
TITLE="Frames of eigenspaces and localization of signal components",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="297-300",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Time-frequency localization, frames of eigenfunctions",
ABSTRACT="We present a construction of frames adapted to a given time-frequency cover
and study certain computational aspects of it. These frames are based on a
family of orthogonal projections that can be used to localize signals in
the time-frequency plane. We compare the effect of the corresponding
orthogonal projections to the traditional time-frequency masking."
}
@INPROCEEDINGS{Bern1307:Lie,
AUTHOR="Swanhild Bernstein",
TITLE="A Lie group approach to diffusive wavelets",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="301-304",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="continuous wavelets; Lie groups; semigroups; homogeneous spaces; Heisenberg
group",
ABSTRACT="The aim of this paper is to give an overview of diffusive wavelets on
compact groups, homogeneous spaces and the Heisenberg group. This approach
is based on Lie groups and representation theory and generalizes well-known
constructions of wavelets on the sphere. The key idea of diffusive wavelets
is to generate a dilation from a diffusive semigroup where as the
translation is the action of a compact group. We give examples for the
construction of diffusive wavelets."
}
@INPROCEEDINGS{Pese1307:Shannon,
AUTHOR="Isaac Pesenson",
TITLE="Shannon Sampling and Parseval Frames on Compact Manifolds",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="305-308",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Homogeneous manifold; Casimir operator; eigenfunctions; frames; cubature
formulas",
ABSTRACT="The paper contains several generalizations of the classical Sampling
Theorem for band limited functions constructed using a self-adjoint second
order differential elliptic operator on a compact homogeneous manifolds."
}
@INPROCEEDINGS{Guil1307:Signal,
AUTHOR="Mijail Guillemard and Holger Boche and Gitta Kutyniok and Friedrich Philipp",
TITLE="Signal Analysis with Frame Theory and Persistent Homology",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="309-312",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Persistent Homology, Frame Theory, Time-Frequency Analysis.",
ABSTRACT="A basic task in signal analysis is to characterize data in a meaningful way
for analysis and classification purposes. Time-Frequency transforms are
powerful strategies for signal decomposition, and important recent
generalizations have been achieved in the setting of frame theory.
In parallel recent developments, tools from algebraic topology,
traditionally developed in purely abstract settings, have provided new
insights in applications to data analysis.
In this report, we investigate some interactions of these tools, both
theoretically and with numerical experiments in order to characterize
signals and their corresponding adaptive frames. We explain basic concepts
in persistent homology as an important new subfield of computational
topology, as well as formulations of time-frequency analysis in frame
theory.
Our objective is to use persistent homology for constructing topological
signatures of signals in the context of frame theory for classification and
analysis purposes. The main motivation for studying these interactions is
to combine the strength of frame theory as a fundamental signal analysis
methodology, with persistent homology as a novel perspective in data
analysis."
}
@INPROCEEDINGS{Case1307:Signal,
AUTHOR="Stephen D. Casey",
TITLE="Signal Adaptive Frame Theory",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="313-316",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Shannon Sampling;Frame Theory",
ABSTRACT="The projection method is an atomic signal decomposition designed for
adaptive frequency band (AFB) and ultra-wide-band (UWB) systems. The method
first windows the signal and then decomposes the signal into a basis via a
continuous-time inner product operation, computing the basis coefficients
in parallel. The windowing systems are key, and we develop systems that
have variable partitioning length, variable roll-off and variable
smoothness. These include systems developed to preserve orthogonality of
any orthonormal systems between adjacent blocks, and almost orthogonal
windowing systems that are more computable/constructible than the
orthogonality preserving systems. The projection method is, in effect, an
adaptive Gabor system for signal analysis. The natural language to express
this structure is frame theory."
}
@INPROCEEDINGS{Puy1307:Joint,
AUTHOR="Gilles Puy and Gabriele Bonanno and Matthias Stuber and Pierre
Vandergheynst",
TITLE="Joint reconstruction of misaligned images from incomplete measurements for
cardiac {MRI}",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="317-320",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="We present a novel method for robust reconstruction of the image of a
moving object from incomplete linear measurements. We assume that only few
measurements of this object can be acquired at different instants and model
the correlation between measurements using global geometric transformations
represented by few parameters. Then, we design a method that is able to
jointly estimate these transformation parameters and an image of the
object, while taking into account possible occlusions of parts of the
object during the acquisitions. The reconstruction algorithm minimizes a
non-convex functional and generates a sequence of estimates converging to a
critical point of this functional. Finally, we show how to apply this
algorithm on a real cardiac acquisition for free breathing coronary
magnetic resonance imaging."
}
@INPROCEEDINGS{Doga1307:Localization,
AUTHOR="Zafer Dogan and Ivana Jovanovic and Thierry Blu and Dimitri {Van De Ville}",
TITLE="Localization of point sources in wave fields from boundary measurements
using new sensing principle",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="321-324",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Sensing principle, finite-rate-of-innovation (FRI), wave equation, source
imaging, inverse problem",
ABSTRACT="We address the problem of localizing point sources in 3D from boundary
measurements of a wave field. Recently, we prosed the sensing principle
which allows extracting volumetric samples of the unknown source
distribution from the boundary measurements. The extracted samples allow a
non-iterative re construction algorithm that can recover the parameters of
the source distribution projected on a 2-D plane in the continuous domain
without any discretization. Here we extend the method for the 3-D
localization of multiple point sources by combining multiple 2-D planar
projections. In particular, we propose a three-step algorithm to retrieve
the locations by means of multiplanar application of the sensing principle.
First, we find the projections of the locations onto several 2-D planes.
Second, we propose a greedy algorithm to pair the solutions in each plane.
Third, we retrieve the 3D locations by least squares regression."
}
@INPROCEEDINGS{Sudh1307:Compressive,
AUTHOR="Prasad Sudhakar and Laurent Jacques and Adriana {Gonzalez Gonzalez} and
Xavier Dubois and Philippe Antoine and Luc Joannes",
TITLE="Compressive Acquisition of Sparse Deflectometric Maps",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="325-328",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="compressive imaging, schlieren deflectometer, total variation, regularized
inverse problem, denoising",
ABSTRACT="Schlieren deflectometry aims at measuring deflections of light rays from
transparent objects, which is subsequently used to characterize the
objects. With each location on a smooth object surface a sparse deflection
map (or spectrum) is associated. In this paper, we demonstrate the
compressive acquisition and reconstruction of such maps, and the usage of
deflection information for object characterization, using a schlieren
deflectometer. To this end, we exploit the sparseness of deflection maps
and we use the framework of spread spectrum compressed sensing. Further, at
a second level, we demonstrate how to use the deflection information
optimally to reconstruct the distribution of refractive index inside an
object, by exploiting the sparsity of refractive index maps in gradient
domain."
}
@INPROCEEDINGS{McEw1307:Fourier,
AUTHOR="Jason McEwen and Boris Leistedt",
TITLE="{Fourier-Laguerre} transform, convolution and wavelets on the ball",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="329-332",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Harmonic analysis, sampling, wavelets, three-dimensional ball",
ABSTRACT="We review the Fourier-Laguerre transform, an alternative harmonic analysis
on the three-dimensional ball to the usual Fourier-Bessel transform. The
Fourier-Laguerre transform exhibits an exact quadrature rule and thus leads
to a sampling theorem on the ball. We study the definition of convolution
on the ball in this context, showing explicitly how translation on the
radial line may be viewed as convolution with a shifted Dirac delta
function. We review the exact Fourier-Laguerre wavelet transform on the
ball, coined flaglets, and show that flaglets constitute a tight frame."
}
@INPROCEEDINGS{Simo1307:Truncation,
AUTHOR="Loic Simon",
TITLE="Truncation Error in Image Interpolation",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="333-336",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="image interpolation, spatial truncation, RMSE,",
ABSTRACT="Interpolation is a fundamental issue in image processing. In this short
paper, we communicate ongoing results concerning the accuracy of two
landmark approaches: the Shannon expansion and the DFT interpolation. Among
all sources of error, we focus on the impact of spatial truncation. Our
estimations are expressed in the form of upper bounds on the Root Mean
Square Error as a function of the distance to the image border. The quality
of these bounds is appraised through experiments driven on natural images."
}
@INPROCEEDINGS{Kirs1307:Identification,
AUTHOR="Hagai Kirshner and John Paul Ward and Michael Unser",
TITLE="Identification of Rational Transfer Functions from Sampled Data",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="341-343",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="We consider the task of estimating an operator from sampled data. The
operator, which is described by a rational transfer function, is applied to
continuous-time white noise and the resulting continuous-time process is
sampled uniformly. The main question we are addressing is whether the
stochastic properties of the time series that originates from the sample
values of the process allows one to determine the operator. We focus on the
autocorrelation property of the process and identify cases for which the
sampling operator is injective. Our approach relies on sampling properties
of almost periodic functions, which together with exponentially decaying
functions, provide the building blocks of the autocorrelation measure. Our
results indicate that it is possible, in principle, to estimate the
parameters of the rational transfer function from sampled data, even in the
presence of prominent aliasing."
}
@INPROCEEDINGS{Ozbe1307:Reconstruction,
AUTHOR="Ali Ozbek and Massimiliano Vassallo and Kemal Ozdemir and Dirk-Jan {van
Manen} and Kurt Eggenberger",
TITLE="Reconstruction of Signals from Highly Aliased Multichannel Samples by
Generalized Matching Pursuit",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="344-347",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Multichannel sampling, aliasing, matching pursuit, compressive sensing",
ABSTRACT="This paper considers the problem of reconstructing a bandlimited signal
from severely aliased multichannel samples. Multichannel sampling in this
context means that the samples are available after the signal has been
filtered by various linear operators. We propose the method of Generalized
Matching Pursuit to solve the reconstruction problem. We illustrate the
potential of the method using synthetic data that could be acquired using
multimeasurement towed-streamer seismic data acquisition technology. A
remarkable observation is that high-fidelity reconstruction is possible
even when the data are uniformly and coarsely sampled, with the order of
aliasing significantly exceeding the number of channels."
}
@INPROCEEDINGS{Pawl1307:Joint,
AUTHOR="Mirek Pawlak",
TITLE="Joint Signal Sampling and Detection",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="348-351",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="joint sampling-detection, parametric signals, nonparametric alternatives",
ABSTRACT="In this paper, we examine the joint signal sampling and detection problem
when noisy samples of a signal are collected in the sequential fashion. In
such a scheme, at the each observation time point we wish to make a
decision that the observed data record represents a signal of the assumed
target form. Moreover, we are able simultaneously to recover a signal when
it departs from the target class. For such a joint signal detection and
recovery setup, we introduce a novel algorithm relying on the smooth
correction of linear sampling schemes. Given a finite frame of noisy
samples of the signal we design a detector being able to test a departure
from a target signal as quickly as possible. Our detector is represented as
a continuous time normalized partial-sum stochastic process, for which we
obtain a functional central limit theorem under weak assumptions on the
correlation structure of the noise. The established limit theorems allow us
to design monitoring algorithms with the desirable level of the probability
of false alarm and able to detect a change with probability approaching
one."
}
@INPROCEEDINGS{Unni1307:Optimal,
AUTHOR="Jayakrishnan Unnikrishnan and Martin Vetterli",
TITLE="On Optimal Sampling Trajectories for Mobile Sensing",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="352-355",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="sampling trajectories, mobile sensing",
ABSTRACT="We study the design of sampling trajectories for stable sampling and
reconstruction of bandlimited spatial fields using mobile sensors. As a
performance metric we use the path density of a set of sampling
trajectories, defined as the total distance traveled by the moving sensors
per unit spatial volume of the spatial region being monitored. We obtain
new results for the problem of designing stable sampling trajectories with
minimal path density, that admit perfect reconstruction of bandlimited
fields. In particular, we identify the set of parallel lines with minimal
path density that contains a stable sampling set for isotropic fields."
}
@INPROCEEDINGS{Yang1307:Phase,
AUTHOR="Fanny Yang and Volker Pohl and Holger Boche",
TITLE="Phase Retrieval via Structured Modulations in {Paley-Wiener} Spaces",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="356-359",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Paley-Wiener spaces, phase retrieval, sampling, Bernstein spaces",
ABSTRACT="This paper considers the recovery of continuous time signals from the
magnitude of its samples. It uses a combination of structured modulation
and oversampling and provides sufficient conditions on the signal and the
sampling system such that signal recovery is possible. In particular, it is
shown that an average sampling rate of four times the Nyquist rate is
sufficient to reconstruct a signal from its magnitude measurements."
}
@INPROCEEDINGS{Bah1307:Energy,
AUTHOR="Bubacarr Bah and Volkan Cevher and Ali Sadeghian",
TITLE="Energy-aware adaptive bi-Lipschitz embeddings",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="360-363",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Dimensionality reduction; Johnson-Lindenstrauss embedding; algorithm;
compressed sensing; deterministic matrix design",
ABSTRACT="We propose a dimensionality reducing matrix design based on training data
with constraints on its Frobenius norm and number of rows. Our design
criteria is aimed at preserving the distances between the data points in
the dimensionality reduced space as much as possible relative to their
distances in original data space. This approach can be considered as a
deterministic Bi-Lipschitz embedding of the data points. We introduce a
scalable learning algorithm, dubbed AMUSE, and provide a rigorous
estimation guarantee by leveraging game theoretic tools. We also provide a
generalization characterization of our matrix based on our sample data. We
use compressive sensing problems as an example application of our problem,
where the Frobenius norm design constraint translates into the sensing
energy."
}
@INPROCEEDINGS{Cevh1307:Randomized,
AUTHOR="Stephen Becker and Volkan Cevher and Anastasios Kyrillidis",
TITLE="Randomized Singular Value Projection",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="364-367",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="Affine rank minimization algorithms typically rely on calculating the
gradient of a data error followed by a singular value decomposition at
every iteration. Because these two steps are expensive, heuristic
approximations are often used to reduce computational burden. To this end,
we propose a recovery scheme that merges the two steps with randomized
approximations, and as a result, operates on space proportional to the
degrees of freedom in the problem. We theoretically establish the
estimation guarantees of the algorithm as a function of approximation
tolerance. While the theoretical approximation requirements are overly
pessimistic, we demonstrate that in practice the algorithm performs well on
the quantum tomography recovery problem."
}
@INPROCEEDINGS{Carr1307:Sparsity,
AUTHOR="Rafael Carrillo and Jason McEwen and Yves Wiaux",
TITLE="On Sparsity Averaging",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="368-371",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Compressed sensing, sparse approximation, sparse models",
ABSTRACT="Recent developments in [1] and [2] introduced a novel regularization method
for compressive imaging in the context of compressed sensing with coherent
redundant dictionaries. The approach relies on the observation that natural
images exhibit strong average sparsity over multiple coherent frames. The
associated reconstruction algorithm, based on an analysis prior and a
reweighted L1 scheme, is dubbed Sparsity Averaging Reweighted Analysis
(SARA). We review these advances and extend associated simulations
establishing the superiority of SARA to regularization methods based on
sparsity in a single frame, for a generic spread spectrum acquisition and
for a Fourier acquisition of particular interest in radio astronomy."
}
@INPROCEEDINGS{Hand1307:Conditions,
AUTHOR="Paul Hand",
TITLE="Conditions for Dual Certificate Existence in Semidefinite Rank-1 Matrix
Recovery",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="372-375",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="semidefinite programming; convex optimization; dual certificate",
ABSTRACT="We study the existence of dual certificates in convex minimization problems
where a rank-1 matrix X0 is to be recovered under semidefinite and linear
constraints. We provide an example where such a dual certificate does not
exist. We prove that dual certificates are guaranteed to exist if the
linear measurement matrices can not be recombined to form something
positive and orthogonal to X0. If the measurements can be recombined in
this way, the problem is equivalent to one with additional linear
constraints. That augmented problem is guaranteed to have a dual
certificate at the minimizer, providing the form of an optimality
certificate for the original problem."
}
@INPROCEEDINGS{Krah1307:Restricted,
AUTHOR="Felix Krahmer and Shahar Mendelson and Holger Rauhut",
TITLE="The restricted isometry property for random convolutions",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="376-379",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Compressed sensing, Restricted Isometry Property, Partial Circulant
Matrices",
ABSTRACT="We present significantly improved estimates for the restricted isometry
constants of partial random circulant matrices as they arise in the matrix
formulation of subsampled convolution with a random pulse. We show that the
required condition on the number $m$ of rows in terms of the sparsity $s$
and the vector length $n$ is $m > C s \log^2 s \log^2 n$."
}
@INPROCEEDINGS{Ward1307:Local,
AUTHOR="Felix Krahmer and Holger Rauhut and Rachel Ward",
TITLE="Local coherence sampling for stable sparse recovery",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="476-480",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="Exact recovery guarantees in compressive sensing often assume incoherence
between the sensing basis and sparsity basis, a strong assumption that is
often unattainable in practice. Here we discuss the notion of local
coherence, and show that by resampling from the sensing basis according to
the local coherence function, stable and robust sparse recovery guarantees
extend to a rich new class of sensing problems beyond incoherent systems.
We discuss particular applications to compressive MRI imaging and
polynomial interpolation."
}
@INPROCEEDINGS{Plan1307:Structured,
AUTHOR="Yaniv Plan",
TITLE="Structured-signal recovery from single-bit measurements",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="481-484",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="1-bit compressed sensing; sparse logistic regression; binary matrix
completion; convex optimization; ell\_1 minimization",
ABSTRACT="1-bit compressed sensing was introduced by Boufounos and Baraniuk in 2008
as a model of extreme quantization; only the sign of each measurement is
retained. Recent theoretical and algorithmic advances, combined with the
ease of hardware implementation, show that it is an effective method of
signal acquisition. Surprisingly, in the high-noise regime there is almost
no information loss from 1-bit quantization. We review and revise recent
results, and compare to closely related statistical problems: sparse binary
regression and binary matrix completion."
}
@INPROCEEDINGS{Schn1307:Dictionary,
AUTHOR="Karin Schnass",
TITLE="Dictionary Identification Results for {K-SVD} with Sparsity Parameter 1",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="485-488",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="dictionary learning; sparse coding; finite samples; K-SVD; sampling
complexity; dictionary identification; minimisation criterion; sparse
representation",
ABSTRACT="In this talk we summarise part of the results from our recent work
\cite{sc13arxiv} and \cite{sc13b}. We give theoretical insights into the
performance of K-SVD, a dictionary learning algorithm that has gained
significant popularity in practical applications, by answering the question
when a dictionary $\dico$ can be recovered as local minimum of the
minimisation criterion underlying K-SVD from a set of training signals
$y\_n=\dico x\_n$. Assuming the training signals are generated from a tight
frame with coefficients drawn from a random symmetric distribution, then in
expectation the generating dictionary can be recovered as a local minimum
of the K-SVD criterion if the coefficient distribution exhibits sufficient
decay. This decay can be characterised by the coherence of the dictionary
and the $\ell\_1$-norm of the coefficients. Further it is demonstrated that
given a finite number of training samples $N$ with probability
$O(\exp(-N^{1-4q}))$ there is a local minimum of the K-SVD criterion within
a radius $O(N^{-q})$ of the generating dictionary."
}
@INPROCEEDINGS{Vint1307:Multivariate,
AUTHOR="Federico Cluni and Danilo Costarelli and Anna Maria Minotti and Gianluca
Vinti",
TITLE="Multivariate sampling Kantorovich operators: approximation and applications
to civil engineering",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="400-403",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Signal and Image reconstruction; sampling-Kantorovich operators;
Approximation;Thermographic images;",
ABSTRACT="In this paper, we present the theory and some new applications of linear,
multivariate, sampling Kantorovich operators. By means of the above
operators, we are able to reconstruct pointwise, continuous and bounded
signals (functions), and to approximate uniformly, uniformly continuous and
bounded functions. Moreover, the reconstruction of signals belonging to
Orlicz spaces are also considered. In the latter case, we show how our
operators can be used to approximate not necessarily continuous
signals/images, and an algorithm for image reconstruction is developed.
Several applications of the theory in civil engineering are obtained.
Thermographic images, such as masonries images, are processed to study the
texture of the buildings, thus to separate the stones from the mortar and
finally a real-world case-study is analyzed in terms of structural
analysis."
}
@INPROCEEDINGS{Levi1307:Number,
AUTHOR="Tatiana Levitina",
TITLE="On the Number of Degrees of Freedom of {Band-Limited} Functions",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="404-407",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="sampling theorem, prolates, band-limited functions, number of degrees of
freedom",
ABSTRACT="The concept of the number of degrees of freedom of band-limited signals is
discussed. Classes of band-limited signals obtained as a result of
successive application of the truncated direct and truncated inverse
Fourier transforms are shown to posses a finite number of degrees of
freedom."
}
@INPROCEEDINGS{Matu1307:Tracing,
AUTHOR="Monika Doerfler and Ewa Matusiak",
TITLE="Tracing Sound Objects in Audio Textures",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="408-411",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="This contribution presents first results on two proposed methods to trace
sound objects within texture sounds. We first discuss what we mean by these
two notions and explain how the properties of a sound that is known to be
textural are exploited in order to detect changes which suggest the
presence of a distinct sound event. We introduce two approaches, one is
based on Gabor multipliers mapping consecutive time-segments of the signal
to each other, the other one on dictionary learning. We present the results
of simulations based on real data."
}
@INPROCEEDINGS{Nam1307:Uncertainty,
AUTHOR="Sangnam Nam",
TITLE="An Uncertainty Principle for Discrete Signals",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="412-415",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="uncertainty principle;time-frequency localization;discrete Fourier
transform",
ABSTRACT="By use of window functions, time-frequency analysis tools like short time
Fourier transform overcome a shortcoming of the Fourier transform and
enable us to study the time-frequency characteristics of signals which
exhibit transient oscillatory behaviours. Since the resulting
representations depend on the choice of the window functions, it is
important to know how they influence the analyses. One crucial question on
a window function is how accurate it permits us to analyze the signals in
the time and frequency domains. In the continuous domain (for functions
defined on the real line), the limit on the accuracy is well-established by
the Heisenberg's uncertainty principle when the time-frequency spread is
measured in terms of the variance measures. However, for the finite
discrete signals (where we consider the discrete Fourier transform), the
uncertainty relation is not as well understood. Our work fills in some of
the gap in the understanding and states uncertainty relation for a subclass
of finite discrete signals. Interestingly, the result is a close parallel
to that of the continuous domain: the time-frequency spread measure is, in
some sense, natural generalization of the variance measure in the
continuous domain, the lower bound for the uncertainty is close to that of
the continuous domain, and the lower bound is achieved approximately by the
`discrete Gaussians'."
}
@INPROCEEDINGS{Rati1307:Efficient,
AUTHOR="Alin Ratiu and Dominique Morche and Arnaud Arias and Bruno Allard and
Xuefang Lin-Shi and Jacques Verdier",
TITLE="Efficient Simulation of Continuous Time Digital Signal Processing {RF}
Systems",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="416-419",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Continuous-time digital signal; Simulation; Non-uniform sampling;
Continuous-time analog-to-digital converter;",
ABSTRACT="A new simulation method for continuous time digital signal processing RF
architectures is proposed. The approach is based on a discrete time
representation of the input signal combined with a linear interpolation.
Detailed theoretical calculations are presented, which prove the efficiency
of the simulation when dealing with RF signals. We show that, compared to a
discrete time simulation, for the same simulation error a decrease of
almost two orders of magnitude is expected in the necessary number of input
samples."
}
@INPROCEEDINGS{Sade1307:Shift,
AUTHOR="Bashir Sadeghi and Runyi Yu",
TITLE="{Shift-Variance} and Cyclostationarity of Linear Periodically
{Shift-Variant} Systems",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="420-423",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="cyclostationarity; generalized sampling processes; linear periodically
shift-variant systems; shift-variance",
ABSTRACT="We study shift-variance and cyclostationarity of linear periodically
shift-variant (LPSV) systems. Both input and output spaces are assumed to
be of continuous-time. We first determine how far an LPSV system is away
from the space of linear shift-invariant systems. We then consider
cyclostationarity of a random process based on its autocorrelation
operator. The results allow us to investigate properties of output of an
LPSV system when its input is a random process. Finally, we analyze
shift-variance and cyclostationarity of generalized sampling-reconstruction
processes."
}
@INPROCEEDINGS{Wolf1307:Constructive,
AUTHOR="Moshe Salhov and Guy Wolf and Amit Bermanis and Amir Averbuch",
TITLE="Constructive sampling for patch-based embedding",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="424-427",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Dictionary construction;Patch processing;Diffusion Maps;Kernel methods",
ABSTRACT="To process high-dimensional big data, we assume that sufficiently small
patches (or neighborhoods) of the data are approximately linear. These
patches represent the tangent spaces of an underlying manifold structure
from which we assume the data is sampled. We use these tangent spaces to
extend the scalar relations that are used by many kernel methods to matrix
relations, which encompass multidimensional similarities between local
neighborhoods in the data. The incorporation of these matrix relations
improves the utilization of kernel-based data analysis methodologies.
However, they also result in a larger kernel and a higher computational
cost of its spectral decomposition. We propose a dictionary construction
that approximates the oversized kernel in this case and its associated
patch-to-tensor embedding. The performance of the proposed dictionary
construction is demonstrated on a super-kernel example that utilizes the
Diffusion Maps methodology together with linear-projection operators
between tangent spaces in the manifold."
}
@INPROCEEDINGS{Schm1307:Constrained,
AUTHOR="Ludwig Schmidt and Chinmay Hegde and Piotr Indyk",
TITLE="The Constrained Earth Mover Distance Model, with Applications to
Compressive Sensing",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="428-431",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="compressive sensing; sparse approximation; earth mover distance",
ABSTRACT="Sparse signal representations have emerged as powerful tools in signal
processing theory and applications, and serve as the basis of the
now-popular field of compressive sensing (CS). However, several practical
signal ensembles exhibit additional, richer structure beyond mere sparsity.
Our particular focus in this paper is on signals and images where, owing to
physical constraints, the positions of the nonzero coefficients do not
change significantly as a function of spatial (or temporal) location. Such
signal and image classes are often encountered in seismic exploration,
astronomical sensing, and biological imaging. Our contributions are
threefold: (i) We propose a simple, deterministic model based on the Earth
Mover Distance that effectively captures the structure of the sparse
nonzeros of signals belonging to such classes. (ii) We formulate an
approach for approximating any arbitrary signal by a signal belonging to
our model. The key idea in our approach is a min-cost max-flow graph
optimization problem that can be solved efficiently in polynomial time.
(iii) We develop a CS algorithm for efficiently reconstructing signals
belonging to our model, and numerically demonstrate its benefits over
state-of-the-art CS approaches."
}
@INPROCEEDINGS{Schn1307:Orlicz,
AUTHOR={Catherine Schnackers and Hartmut {F{\"u}hr}},
TITLE="Orlicz Modulation Spaces",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="432-435",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="In this work we extend the definition of modulation spaces associated to
Lebesgue spaces to Orlicz spaces and mixed-norm Orlicz spaces. We give the
definition of the Orlicz spaces $L^\Phi$, a generalisation of the $L^p$
spaces of Lebesgue. Therefore we characterise the Young function $\Phi$ and
give some basic properties of this spaces. We collect some facts about this
spaces that we need for the time frequency analysis, then we introduce the
Orlicz modulation spaces. Finally we present a discretisation of the Orlicz
space and mixed-norm Orlicz space and a characterisation of the modulation
space by discretisation."
}
@INPROCEEDINGS{Sekm1307:Binary,
AUTHOR="Ali Sekmen and Akram Aldroubi",
TITLE="Binary Reduced Row Echelon Form Approach for Subspace Segmentation",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="436-439",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="This paper introduces a subspace segmentation and data clustering method
for a set of data drawn from a union of subspaces. The proposed method
works perfectly in absence of noise, i.e., it can find the number of
subspaces, their dimensions, and an orthonormal basis for each subspace.
The effect of noise on this approach depends on the noise level and
relative positions of subspaces. We provide a comprehensive performance
analysis in presence of noise and outliers."
}
@INPROCEEDINGS{Shab1307:Missing,
AUTHOR="Gil Shabat and Yaniv Shmueli and Amir Averbuch",
TITLE="Missing Entries Matrix Approximation and Completion",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="440-443",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="matrix completion, matrix approximation, spectral norm, Ky-Fan norm",
ABSTRACT="We describe several algorithms for matrix completion and matrix
approximation when only some of its entries are known. The approximation
constraint can be any whose approximated solution is known for the full
matrix. For low rank approximations, similar algorithms appear recently in
the literature under different names. In this work, we introduce new
theorems for matrix approximation and show that these algorithms can be
extended to handle different constraints such as nuclear norm, spectral
norm, orthogonality constraints and more that are different than low rank
approximations. As the algorithms can be viewed from an optimization point
of view, we discuss their convergence to global solution for the convex
case. We also discuss the optimal step size and show that it is fixed in
each iteration. In addition, the derived matrix completion flow is robust
and does not require any parameters. This matrix completion flow is
applicable to different spectral minimizations and can be applied to
physics, mathematics and electrical engineering problems such as data
reconstruction of images and data coming from PDEs such as Helmholtz's
equation used for electromagnetic waves."
}
@INPROCEEDINGS{Shmu1307:Using,
AUTHOR="Yaniv Shmueli and Tuomo Sipola and Gil Shabat and Amir Averbuch",
TITLE="Using Affinity Perturbations to Detect Web Traffic Anomalies",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="444-447",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="perturbation theory, eigenvalue problem, diffusion maps, dimensionality
reduction, anomaly detection, web traffic",
ABSTRACT="The initial training phase of machine learning algorithms is usually
computationally expensive as it involves the processing of huge matrices.
Evolving datasets are challenging from this point of view because changing
behavior requires updating the training. We propose a method for updating
the training profile efficiently and a sliding window algorithm for online
processing of the data in smaller fractions. This assumes the data is
modeled by a kernel method that includes spectral decomposition. We
demonstrate the algorithm with a web server request log where an actual
intrusion attack is known to happen. Updating the kernel dynamically using
a sliding window technique, prevents the problem of single initial training
and can process evolving datasets more efficiently."
}
@INPROCEEDINGS{Kuma1307:Finite,
AUTHOR="Srikanth Tenneti and Animesh Kumar and Abhay Karandikar",
TITLE="Finite Rate of Innovation Signals: Quantization Analysis with
{Resistor-Capacitor} Acquisition Filter",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="448-451",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="signal reconstruction; signal sampling; quantization; approximation error;
sampling methods;",
ABSTRACT="Finite rate of innovation or FRI signals, which are usually not
bandlimited, have been studied as an alternate model for signal sampling
and reconstruction. Sampling and perfect reconstruction of FRI signals was
first presented by Vetterli, Marziliano, and Blu.
A typical FRI reconstruction algorithm requires solving for FRI signal
parameters from a power-sum series. This in turn requires annihilation
filters and root-finding techniques. These non-linear steps complicate the
analysis of FRI signal reconstruction in the presence of quantization. In
this work, we introduce a resistor-capacitor filter bank for sample
acquisition of FRI signal and an associated signal reconstruction scheme
which uses much simpler operations than those of the existing techniques.
This simplification allows us to analyze the effect of quantization noise.
However, the sampling-rate required for our scheme is larger than the
minimum sampling-rate of FRI signals."
}
@INPROCEEDINGS{Tyag1307:Tangent,
AUTHOR="Hemant Tyagi and Elif Vural and Pascal Frossard",
TITLE="Tangent space estimation bounds for smooth manifolds",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="452-455",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="Many manifold learning methods require the estimation of the tangent space
of the manifold at a point from locally available data samples. Local
sampling conditions such as (i) the size of the neighborhood and (ii) the
number of samples in the neighborhood affect the performance of learning
algorithms. In this paper, we propose a theoretical analysis of local
sampling conditions for the estimation of the tangent space at a point P
lying on an m-dimensional Riemannian manifold S in R^n. Assuming a smooth
embedding of S in R^n, we estimate the tangent space by performing a
Principal Component Analysis (PCA) on points sampled from the neighborhood
of P on S. Our analysis explicitly takes into account the second order
properties of the manifold at P, namely the principal curvatures as well as
the higher order terms. Considering a random sampling framework, we
leverage recent results from random matrix theory to derive local sampling
conditions for an accurate estimation of tangent subspace. Our main results
state that the width of the sampling region in the tangent space
guaranteeing an accurate estimation is inversely proportional to the
manifold dimension, curvature, and the square root of the ambient space
dimension. At the same time, we show that the number of samples increases
quadratically with the manifold dimension and logarithmically with the
ambient space dimension."
}
@INPROCEEDINGS{Wang1307:Null,
AUTHOR="Rongrong Wang and Xuemei Chen and Haichao Wang",
TITLE="A null space property approach to compressed sensing with frames",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="456-459",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="compressed sensing, dictionary, null space property",
ABSTRACT="An interesting topic in compressive sensing concerns problems of sensing
and recovering signals with sparse representations in a dictionary. In this
note, we study conditions of sensing matrices $A$ for the
$\ell^1$-synthesis method to accurately recovery sparse, or nearly sparse
signals in a given dictionary $D$. In particular, we propose a dictionary
based null space property (D-NSP) which, to the best of our knowledge, is
the first sufficient and necessary condition for the success of the
$\ell^1$ recovery. This new property is then utilized to detect some of
those dictionaries whose sparse families cannot be compressed universally.
Moreover, when the dictionary is full spark, we show that $AD$ being NSP,
which is well-known to be only sufficient for stable recovery via
$\ell^1$-synthesis method, is indeed necessary as well."
}
@INPROCEEDINGS{Wies1307:Irregular,
AUTHOR="Thomas Wiese and Laurent Demaret",
TITLE="Irregular Sampling of the Radon Transform of Bandlimited Functions",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="460-463",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Radon transform; Irregular sampling; Bandlimited functions",
ABSTRACT="We provide conditions for exact reconstruction of a bandlimited function
from irregular polar samples of its Radon transform. First, we prove that
the Radon transform is a continuous L2 -operator for certain classes of
bandlimited signals. We then show that the Beurling-Malliavin condition for
the radial sampling density ensures existence and uniqueness of a solution.
Moreover, Jaffard's density condition is sufficient for stable
reconstruction."
}
@INPROCEEDINGS{Zhel1307:Spline,
AUTHOR={Valery Zheludev and Pekka {Neittaanm{\"a}ki} and Amir Averbuch},
TITLE="Spline-based frames for image restoration",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="464-467",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="spline;frame;filter banck; Bregman iteration",
ABSTRACT="We present a design scheme to generate tight and semi-tight frames in the
space of discrete-time periodic signals, which are originated from
four-channel perfect reconstruction periodic filter banks. The filter banks
are derived from interpolating and quasi-interpolating polynomial splines.
Each filter bank comprises one linear phase low-pass filter (in most cases
interpolating) and one high-pass filter, whose magnitude response mirrors
that of a low-pass filter. In addition, these filter banks comprise two
band-pass filters. In the semi-tight frames case, all the filters have
linear phase and (anti)symmetric impulse response, while in the tight frame
case, some of band-pass filters are slightly asymmetric. We introduce the
notion of local discrete vanishing moments (LDVM). In the tight frame case,
analysis framelets coincide with their synthesis counterparts. However, in
the semi-tight frames, we have the option to swap LDVM between synthesis
and analysis framelets. The design scheme is generic and it enables us to
design framelets with any number of LDVM. The computational complexity of
the framelet transforms, which consists of calculation of the forward and
the inverse fast Fourier transforms and simple arithmetic operations,
practically does not depend on the number of LDVM and on the size of the
impulse response of filters . The designed frames are used for restoration
of images, which are degraded by blurring, random noise and missing pixels.
The images were restored by the application of the Split Bregman Iterations
method. I"
}
@INPROCEEDINGS{Zör1307:Noise,
AUTHOR={Henning {Z{\"o}rlein} and Dejan Lazich and Martin Bossert},
TITLE="On the {Noise-Resilience} of {OMP} with {BASC-Based} Low Coherence Sensing
Matrices",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="468-471",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Compressed Sensing; Coherence; Spherical Codes; Sensing Matrices; OMP;
Noise",
ABSTRACT="In Compressed Sensing (CS), measurements of a sparse vector are obtained by
applying a sensing matrix. With the means of CS, it is possible to
reconstruct the sparse vector from a small number of such measurements. In
order to provide reliable reconstruction also for less sparse vectors,
sensing matrices are desired to be of low coherence. Motivated by this
requirement, it was recently shown that low coherence sensing matrices can
be obtained by Best Antipodal Spherical Codes (BASC). In this paper, the
noise-resilience of the Orthogonal Matching Pursuit (OMP) used in
combination with low coherence BASC-based sensing matrices is investigated."
}
@INPROCEEDINGS{Datt1307:Tight,
AUTHOR="Somantika Datta and Enrico Au-Yeung",
TITLE="Tight frames in spiral sampling",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="472-475",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="The paper deals with the construction of Parseval tight frames for the
space of square integrable functions whose domain is the ball of radius R
and centered at the origin. The focus is on Fourier frames on a spiral.
Starting with a Fourier frame on a spiral, a Parseval tight frame that
spans the same space can then be obtained by a symmetric approximation of
the original Fourier frame."
}
@INPROCEEDINGS{Wolf1307:Measure,
AUTHOR="Amit Bermanis and Guy Wolf and Amir Averbuch",
TITLE="Measure-based diffusion kernel methods",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="489-492",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Diffusion Maps;Diffusion-base kernel;Kernel methods;Measure-based
information.",
ABSTRACT="A commonly used approach for analyzing massive high dimensional datasets is
to utilize diffusion-based kernel methods. The kernel in these methods is
based on a Markovian diffusion process, whose transition probabilities are
determined by local similarities between data points. When the data lies on
a low dimensional manifold, the diffusion distances according to this
kernel encompass the geometry of the manifold. In this paper, we present a
generalized approach for defining diffusion-based kernels by incorporating
measure-based information, which represents the density or distribution of
the data, together with its local distances. The generalized construction
does not require an underlying manifold to provide a meaningful kernel
interpretation but assumes a more relaxed assumption that the measure and
its support are related to a locally low dimensional nature of the analyzed
phenomena."
}
@INPROCEEDINGS{Lemv1307:Spectral,
AUTHOR="Felix Krahmer and Gitta Kutyniok and Jakob Lemvig",
TITLE="Spectral properties of dual frames",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="493-496",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="dual frames, dual frames, frame theory, singular values, spectrum of
frames, tight frames",
ABSTRACT="We study spectral properties of dual frames of a given finite frame. We
give a complete characterization for which spectral patterns of dual frames
are possible for a fixed frame. For many cases, we provide simple explicit
constructions for dual frames with a given spectrum, in particular, if the
constraint on the dual is that it be tight."
}
@INPROCEEDINGS{Ayaz1307:Sparse,
AUTHOR="Ulas Ayaz and Holger Rauhut",
TITLE="Sparse Recovery with Fusion Frames via {RIP}",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="497-500",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Compressive Sensing; Fusion Frames; Random Matrices",
ABSTRACT="We extend ideas from compressed sensing to a structured sparsity model
related to fusion frames. We present theoretical results concerning the
recovery of sparse signals in a fusion frame from undersampled
measurements. We provide both nonuniform and uniform recovery guarantees.
The novelty of our work is to exploit an incoherence property of the fusion
frame which allows us to reduce the number of measurements needed for
sparse recovery."
}
@INPROCEEDINGS{Bile1307:Blind,
AUTHOR="Cagdas Bilen and Gilles Puy and R{\'e}mi Gribonval and Laurent Daudet",
TITLE="Blind Sensor Calibration in Sparse Recovery Using Convex Optimization",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="501-504",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="compressed sensing; calibration; dictionary learning; blind signal
separation; sparse recovery",
ABSTRACT="We investigate a compressive sensing system in which the sensors introduce
a distortion to the measurements in the form of unknown gains. We focus on
{\em blind} calibration, using measures performed on a few unknown (but
sparse) signals. We extend our earlier study on real positive gains to two
generalized cases (signed real-valued gains; complex-valued gains), and
show that the recovery of unknown gains together with the sparse signals is
possible in a wide variety of scenarios. The simultaneous recovery of the
gains and the sparse signals is formulated as a convex optimization problem
which can be solved easily using off-the-shelf algorithms. Numerical
simulations demonstrate that the proposed approach is effective provided
that sufficiently many (unknown, but sparse) calibrating signals are
provided, especially when the sign or phase of the unknown gains are not
completely random."
}
@INPROCEEDINGS{Boye1307:Sampling,
AUTHOR="Claire Boyer and J{\'e}r{\'e}mie Bigot and Pierre Armand Weiss",
TITLE="Sampling by blocks of measurements in Compressed Sensing",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="505-508",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="Various acquisition devices impose sampling blocks of measurements. A
typical example is parallel magnetic resonance imaging (MRI) where several
radio-frequency coils simultaneously acquire a set of Fourier modulated
coefficients. We study a new random sampling approach that consists in
selecting a set of blocks that are predefined by the application of
interest. We provide theoretical results on the number of blocks that are
required for exact sparse signal reconstruction. We finish by illustrating
these results on various examples, and discuss their connection to the
literature on CS."
}
@INPROCEEDINGS{Chau1307:Travelling,
AUTHOR="Nicolas Chauffert and Philippe Ciuciu and Jonas Kahn and Pierre Armand
Weiss",
TITLE="Travelling salesman-based variable density sampling",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="509-512",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="compressed sensing; travelling salesman problem; variable density sampling",
ABSTRACT="Compressed sensing theory indicates that selecting a few measurements
independently at random is a near optimal strategy to sense sparse or
compressible signals. This is infeasible in practice for many acquisition
devices that acquire samples along continuous trajectories (e.g., radial,
spiral, ...). Examples include magnetic resonance imaging (MRI) or
radio-interferometry. In this paper, we propose to generate continuous
sampling trajectories by drawing a small set of measurements independently
and joining them using a travelling salesman problem solver. Our
contribution lies in the theoretical derivation of the appropriate
probability density of the initial drawings. Preliminary simulation results
show that this strategy is as efficient as independent drawings while being
implementable on real acquisition systems."
}
@INPROCEEDINGS{Shut1307:Incremental,
AUTHOR="Dmitriy Shutin and Wei Wang and Jost Thomas",
TITLE="Incremental Sparse Bayesian Learning for Parameter Estimation of
Superimposed Signals",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="513-516",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="sparse Bayesian learning, superimposed signals, parameter estimation",
ABSTRACT="This work discuses a novel algorithm for joint sparse estimation of
superimposed signals and their parameters. The proposed method is based in
two concepts: a variational Bayesian version of the incremental sparse
Bayesian learning (SBL) - fast variational SBL - and a variational Bayesian
approach to parameter estimation of superimposed signal models. Both
schemes estimate the unknown parameters by minimizing the variational lower
bound on model evidence; also, these optimizations are performed
incrementally with respect to the parameters of single component. It is
demonstrated that these estimations can be naturally unified under the
framework of variational Bayesian inference. This allows, on the one hand,
for an adaptive dictionary design for FV-SBL schemes, and, on the other
hand, for a fast superresolution approach to parameter estimation of
superimposed signals. The experimental evidence collected with synthetic
data as well as with estimation results for measured multipath channels
demonstrate the effectiveness of the proposed algorithm."
}
@INPROCEEDINGS{Wang1307:Sparse,
AUTHOR="Thomas Strohmer and Haichao Wang",
TITLE="Sparse {MIMO} Radar with Random Sensor Arrays and Kerdock Codes",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="517-520",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Sparsity, Radar, Compressive Sensing, Random Sensor Arrays, MIMO, Kerdock
Codes",
ABSTRACT="We derive a theoretical framework for the recoverability of targets in the
azimuth-range-Doppler domain using random sensor array and tools developed
in the area of compressive sensing. In one manifestation of our theory we
use Kerdock codes as transmission waveforms and exploit some of their
peculiar properties in our analysis. Not only our result is the first
rigorous mathematical theory for the detection of moving targets using
random sensor arrays, but also the transmitted waveforms satisfy a variety
of properties that are very desirable and important from a practical
viewpoint."
}
@INPROCEEDINGS{Mön1307:Sampling,
AUTHOR={Holger Boche and Ullrich {M{\"o}nich}},
TITLE="Sampling and Reconstruction of Bandlimited {BMO-Functions}",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="521-524",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="sampling; BMO function; sine-type function",
ABSTRACT="Functions of bounded mean oscillation (BMO) play an important role complex
function theory and harmonic analysis. In this paper a sampling theorem for
bandlimited BMO-functions is derived for sampling points that are the zero
sequence of some sine-type function. The class of sine-type functions is
large and, in particular, contains the sine function, which corresponds to
the special case of equidistant sampling. It is shown that the sampling
series is locally uniformly convergent if oversampling is used. Without
oversampling, the local approximation error is bounded."
}
@INPROCEEDINGS{Kuma1307:Bandlimited,
AUTHOR="Animesh Kumar",
TITLE="Bandlimited Signal Reconstruction From the Distribution of Unknown Sampling
Locations",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="528-531",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="signal reconstruction; signal sampling; sampling methods; distortion; mean
square error methods",
ABSTRACT="We study the reconstruction of bandlimited fields from samples taken at
unknown but statistically distributed sampling locations. The setup is
motivated by distributed sampling where precise knowledge of sensor
locations can be difficult.
Periodic one-dimensional bandlimited fields are considered for sampling.
Perfect samples of the field at independent and identically distributed
locations are obtained. The statistical realization of sampling locations
is not known. First, it is shown that a bandlimited field cannot be
uniquely determined with samples taken at statistically distributed but
unknown locations, even if the number of samples is infinite. Next, it is
assumed that the order of sample locations is known. In this case, using
insights from order-statistics, an estimate for the field with useful
asymptotic properties is designed. Distortion (mean-squared error) and
central-limit are established for this estimate."
}
@INPROCEEDINGS{Lake1307:Sampling,
AUTHOR="Joseph Lakey and Jeffrey Hogan",
TITLE="Sampling aspects of approximately time-limited multiband and bandpass
signals",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="532-535",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="prolate; bandlimited; Paley-Wiener space; multiband signal; EEG; phase
synchrony",
ABSTRACT="We provide an overview of recent progress regarding the role of sampling in
the study of signals that are in the image of a bandpass or multiband
frequency limiting operation and have most of their energies concentrated
in a given time interval. First we address the question of approximation of
a time- and band-limited signal on its essential time support by a finite
sinc series. Next we consider a method by which essentially time limited
multiband signals can be approximated as superpositions of eigenfunctions
of time- and band-limiting to each separate band. Finally we consider a
means to approximate essentially time-limited bandpass signals. In this
case we present a new phase-locking metric that arises in the study of EEG
signals."
}
@INPROCEEDINGS{Rzep1307:Recovery,
AUTHOR="Dominik Rzepka and Marek Miskowicz and Anna Gryboś and Dariusz Koscielnik",
TITLE="Recovery of Bandlimited Signal Based on Nonuniform Derivative Sampling",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="536-539",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="nonuniform sampling, derivative sampling, event-based sampling",
ABSTRACT="The paper focuses on the perfect recovery of band- limited signals from
nonuniform samples of the signal and its derivatives. The main motivation
to address signal recovery using nonuniform derivative sampling is a
reduction of mean sampling frequency under Nyquist rate which is a critical
issue in event-based signal processing chains with wireless link. In
particular, we introduce a set of reconstructing functions for nonuniform
derivative sampling as an extension of relevant set of reconstructing
functions derived by Linden and Abramson for uniform derivative sampling.
An example of signal recovery using the first derivative is finally
reported."
}
@INPROCEEDINGS{Tamb1307:Approximation,
AUTHOR="Gert Tamberg and Andi Kivinukk",
TITLE="Approximation by Shannon sampling operators in terms of an averaged modulus
of smoothness",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="540-543",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Sampling operators, averaged modulus of smoothness, order of approximation",
ABSTRACT="The aim of this paper is to study the approximation properties of
generalized sampling operators in L^p(R) in terms of an averaged modulus of
smoothness."
}
@INPROCEEDINGS{Chiu1307:Digital,
AUTHOR="Yun Chiu",
TITLE="Digital Calibration of {SAR} {ADC}",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="544-547",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="SAR ADC; digital background calibration; DAC mismatch; bit weight;
sub-binary redundancy",
ABSTRACT="Four techniques for digital background calibration of SAR ADC are presented
and compared. Sub-binary redundancy is the key to the realization of these
techniques. Some experimental and simulation results are covered to support
the effectiveness of these techniques."
}
@INPROCEEDINGS{Chen1307:Trend,
AUTHOR="Mike Shuo-Wei Chen",
TITLE="Trend of {High-Speed} {SAR} {ADC} towards {RF} Sampling",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="548-551",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="One emerging trend of high-speed low-power ADC design is to leverage the
successive approximation (SAR) topology. It has successfully advanced the
power efficiency by orders of magnitude over the past decade. Given the
nature of SAR algorithm, the conversion speed is intrinsically slow
compared to other high-speed ADC architectures, and yet minimal static
power is required due to the mostly digital implementation. This paper
examines various speed enhancement techniques that enable SAR ADCs towards
RF sampling, i.e. >GS/s sampling rate with >GHz input bandwidth, while
maintaining low power and area consumption. It is expected to play a
crucial role in the future energy-constrained wideband system."
}
@INPROCEEDINGS{Lin1307:Multi,
AUTHOR="Ying-Zu Lin and Ya-Ting Shyu and Che-Hsun Kuo and Guan-Ying Huang and
Chun-Cheng Liu and Soon-Jyh Chang",
TITLE="{Multi-Step} Switching Methods for {SAR} {ADCs}",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="552-555",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="This paper presents multi-step capacitor switching methods for SAR ADCs
based on precharge with floating capacitors and charge sharing. The
proposed switching methods further reduce the transient power of the split
monotonic switching method (an improved version of the monotonic switching
method). Compared to the split monotonic switching, adding charge sharing
achieves around 50\% reduction in switching power. Using precharge with
floating capacitors and charge sharing simultaneously, the switching power
reduces around 75\%. The proposed switching methods do not require
additional intermediate reference voltages."
}
@INPROCEEDINGS{Murm1307:Use,
AUTHOR="Boris Murmann",
TITLE="On the use of redundancy in successive approximation {A/D} converters",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="556-559",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="In practical realizations of sequential (or pipelined) A/D converters, some
form of redundancy is typically employed to help absorb imperfection in the
underlying circuit. The purpose of this paper is to review the various ways
in which redundancy has been used in successive approximating register
(SAR) ADCs, and to connect findings from the information theory community
to ideas that drive modern hardware realizations."
}
@INPROCEEDINGS{Huan1307:Considerations,
AUTHOR="Hai Huang and Xiaoyang Wang and Qiang Li",
TITLE="Design Considerations of {Ultra-Low-Voltage} {Self-Calibrated} {SAR} {ADC}",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="560-563",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="ADC, SAR, ultra low voltage, low power, self-calibration, high resolution.",
ABSTRACT="This paper discusses the design of 0.5V 12bit successive approximation
register (SAR) analog-to-digital converter (ADC) with focus on the
considerations of self calibration at low supply voltage. Relationships
among noises of comparators and overall ADC performance are studied.
Moreover, an ultra-low-leakage switch is demonstrated in a 0.13μm CMOS
process and an improved process of measuring mismatch is proposed to
alleviate the charge injection of sampling switch. Simulation shows the ADC
achieves an ENOB of 11.4b and a SFDR of 90dB near Nyquist rate with
capacitor mismatch up to 3\%. At 12b 1MS/s, the ADC exhibits an FOM of
13.2fJ/step under 0.5V supply voltage."
}
@INPROCEEDINGS{Ehle1307:Phase,
AUTHOR="Martin Ehler and Stefan Kunis",
TITLE="Phase retrieval using time and Fourier magnitude measurements",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="564-567",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Phase retrieval, Fourier transform, Golomb rulers",
ABSTRACT="We discuss the reconstruction of a finite-dimensional signal from the
absolute values of its Fourier coefficients. In many optical experiments
the signal magnitude in time is also available. We combine time and
frequency magnitude measurements to obtain closed reconstruction formulas.
Random measurements are discussed to reduce the number of measurements."
}
@INPROCEEDINGS{Nest1307:Fast,
AUTHOR="Franziska Nestler and Daniel Potts",
TITLE="Fast Ewald summation under 2d- and 1d-periodic boundary conditions based on
{NFFTs}",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="568-571",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="Ewald summation has established as basic element of fast algorithms
evaluating the Coulomb interaction energy of charged systems subject to
periodic boundary conditions. In this context particle mesh routines, as
the P3M method, and the P2NFFT, which is based on nonequispaced fast
Fourier transforms (NFFT), should be mentioned. In this paper we present a
new approach for the efficient calculation of the Coulomb interaction
energy subject to mixed boundary conditions based on NFFTs."
}
@INPROCEEDINGS{Kuni1307:Sparse,
AUTHOR="Daniel Potts and Stefan Kunis and Sabine Heider and Michael Veit",
TITLE="A sparse Prony {FFT}",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="572-575",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="sparse Fast Fourier Transform; sFFT; Prony-like methods",
ABSTRACT="We describe the application of Prony-like reconstruction methods to the
problem of the sparse Fast Fourier transform (sFFT). In particular, we
adapt both important parts of the sFFT, quasi random sampling and filtering
techniques, to Prony-like methods."
}
@INPROCEEDINGS{Volk1307:Taylor,
AUTHOR="Toni Volkmer",
TITLE="Taylor and rank-1 lattice based nonequispaced fast Fourier transform",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="576-579",
DAYS=1,
MONTH=jul,
YEAR=2013,
ABSTRACT="The nonequispaced fast Fourier transform (NFFT) allows the fast approximate
evaluation of trigonometric polynomials with frequencies supported on full
box-shaped grids at arbitrary sampling nodes. Due to the curse of
dimensionality, the total number of frequencies and thus, the total
arithmetic complexity can already be very large for small refinements at
medium dimensions. In this paper, we present an approach for the fast
approximate evaluation of trigonometric polynomials with frequencies
supported on symmetric hyperbolic cross index sets at arbitrary sampling
nodes. This approach is based on Taylor expansion and rank-1 lattice
methods. We prove error estimates for the approximation and present
numerical results."
}
@INPROCEEDINGS{Yomd1307:Decoupling,
AUTHOR="Yosef Yomdin and Dmitry Batenkov and Niv Sarig",
TITLE="Decoupling of Fourier Reconstruction System for Shifts of Several Signals",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="580-583",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Shifts of signals; Fourier samples; Prony system, decoupling, non-uniform
sampling",
ABSTRACT="We consider the problem of ``algebraic reconstruction'' of linear
combinations of shifts of several signals $f\_1,\ldots,f\_k$ from the
Fourier samples. For each $r=1,\ldots,k$ we choose sampling set $S\_r$ to
be a subset of the common set of zeroes of the Fourier transforms ${\cal
F}(f\_\l), \ \l \ne r$, on which ${\cal F}(f\_r)\ne 0$. We show that in
this way the reconstruction system is reduced to $k$ separate systems, each
including only one of the signals $f\_r$. Each of the resulting systems is
of a ``generalized Prony'' form. We discuss the problem of unique
solvability of such systems, and provide some examples."
}
@INPROCEEDINGS{Amin1307:Optimal,
AUTHOR="Arash Amini",
TITLE="Optimal Interpolation Laws for Stable {AR(1)} Processes",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="380-383",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Alpha-stable distribution, Autoregressive process, Interpolation",
ABSTRACT="In this paper, we focus on the problem of interpolating a continuous-time
AR(1) process with stable innovations using minimum average error
criterion. Stable innovations can be either Gaussian or non-Gaussian. In
the former case, the optimality of the exponential splines is well
understood. For non-Gaussian innovations, however, the problem has been all
too often addressed through Monte Carlo methods. In this paper, based on a
recent non-Gaussian stochastic framework, we revisit the AR(1) processes in
the context of stable innovations and we derive explicit expressions for
the optimal interpolator. We find that the interpolator depends on the
stability index of the innovation and is linear for all stable laws,
including the Gaussian case. We also show that the solution can be
expressed in terms of exponential splines."
}
@INPROCEEDINGS{DaSi1307:Hierarchical,
AUTHOR="Curt {Da Silva} and Felix J. Herrmann",
TITLE="Hierarchical Tucker Tensor Optimization - Applications to Tensor Completion",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="384-387",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="structured tensor; hierarchical tucker; differential geometry; manifold
optimization; tensor completion; multidimensional sampling",
ABSTRACT="In this work, we develop an optimization framework for problems whose
solutions are well-approximated by Hierarchical Tucker tensors, an
efficient structured tensor format based on recursive subspace
factorizations. Using the differential geometric tools presented here, we
construct standard optimization algorithms such as Steepest Descent and
Conjugate Gradient, for interpolating tensors in HT format. We also
empirically examine the importance of one's choice of data organization in
the success of tensor recovery by drawing upon insights from the Matrix
Completion literature. Using these algorithms, we recover various seismic
data sets with randomly missing source pairs."
}
@INPROCEEDINGS{Toro1307:Estimation,
AUTHOR="Anatoli Torokhti and Phil Howlett and Hamid Laga",
TITLE="Estimation of large data sets on the basis of sparse sampling",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="388-391",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Sparse sampling, Wiener filtering",
ABSTRACT="We propose a new technique which allows us to estimate any random signal
from a large set of noisy observed data on the basis of samples of only a
few reference signals."
}
@INPROCEEDINGS{Vura1307:Analysis,
AUTHOR="Elif Vural and Pascal Frossard",
TITLE="Analysis of Hierarchical Image Alignment with Descent Methods",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="392-395",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Image registration; image smoothing; gradient-descent; performance analysis",
ABSTRACT="We present a performance analysis for image registration with gradient
descent methods. We consider a multiscale registration setting where the
global 2-D translation between a pair of images is estimated by smoothing
the images and minimizing the distance between their intensity functions
with gradient descent. We focus in particular on the effect of low-pass
filtering on the alignment performance. We adopt an analytic representation
for images and analyze the well-behavedness of the distance function by
estimating the neighborhood of translations for which the distance function
is free of undesired local minima. This corresponds to the set of
translation vectors that are correctly computable with a simple gradient
descent minimization. We show that the area of this neighborhood increases
at least quadratically with the filter size, which justifies the use of
smoothing in image registration with local optimizers. We finally use our
results in the design of a regular multiscale grid in the translation
parameter domain that has perfect alignment guarantees."
}
@INPROCEEDINGS{Cohe1307:Spectrum,
AUTHOR="Deborah Cohen and Yonina C. Eldar",
TITLE="Spectrum Reconstruction from {Sub-Nyquist} Sampling of Stationary Wideband
Signals",
BOOKTITLE="10th international conference on Sampling Theory and Applications (SampTA
2013)",
ADDRESS="Bremen, Germany",
PAGES="396-399",
DAYS=1,
MONTH=jul,
YEAR=2013,
KEYWORDS="Cognitive Radio; Sub-Nyquist Sampling; Spectrum Estimation",
ABSTRACT="In light of the ever-increasing demand for new spectral bands and the
underutilization of those already allocated, the new concept of Cognitive
Radio (CR) has emerged. Opportunistic users could exploit temporarily
vacant bands after detecting the absence of activity of their owners. One
of the most crucial tasks in the CR cycle is therefore spectrum sensing and
detection which has to be precise and efficient. Yet, CRs typically deal
with wideband signals whose Nyquist rates are very high. In this paper, we
propose to reconstruct the spectrum of such signals from sub-Nyquist
samples in order to perform detection. We consider both sparse and non
sparse signals as well as blind and non blind detection in the sparse case.
For each one of those scenarii, we derive the minimal sampling rate
allowing perfect reconstruction of the signal spectrum in a noise-free
environment and provide recovery techniques. The simulations shows spectrum
recovery at the minimal rate in noise-free settings."
}