# Tutorials

## Monday Morning (10:00 - 13:30)

### Signal Processing for Synthesis Aperture Radio Telescopes

*by Amir Leshem*

As evidenced by recent premier journal publications in the signal processing area and leading astronomical and astrophysical journals, this subject is of mutual interest to the signal and image processing communities as well as the astronomical community. This common emphasis is based on several new large international research and development projects for constructing radio telescopes (SKA, LOFAR, ALMA). LOFAR is currently the largest instrument in terms of the number of antenna elements (~6000), and SKA will be 10 fold larger in terms of total collecting area. These new instruments will rely heavily on advanced signal processing techniques, many of which are still in the research phase. Among the problems that are most critical are ionospheric calibration, very high dynamic range imaging with sub-nyquist sampling and the introduction of novel detection technique that combine the data with the background physics. This tutorial is intended to focus the signal processing activity in this field to the most challenging tasks facing the designer of the instruments, as well as the associated data analysis tasks.

### Bio-Inspired Signal Processing

*by Sergio Barbarossa*

There is strong trend, in current research on communication and sensor networks, to study selforganizing, self-healing systems. This poses great challenges to the research on decentralized systems, but at the same offers great potentials for future developments, especially in view of the current trend towards miniaturized systems. Even if the development of self-organizing systems is probably at the beginning, biological systems offers many examples of self-organization and selfhealing. This is as testified, for example, by swarming behaviors, brain activity, and so on. It is then of great interest to derive mathematical models of biological systems and see how they can suggest novel design tools for engineers. Signal Processing can play a big role in this cross-fertilization, as it can help to find out manageable mathematical problems, study their behavior and test the performance in the presence of disturbances. The challenge is to establish a cross-fertilization of ideas from biological to artificial systems, as well as to help understanding biological systems as such. The aim of this tutorial is to review some of the mathematical models underlying simple biological systems and then show some examples of adaptation of these models to solve engineering problems, such as distributed sensing and decentralized resource allocation in cognitive radios.

### Variational Methods for Computer Vision

*by Daniel Cremers*

Variational methods are among the most classical and established methods to solve a multitude of problems arising in computer vision and image processing. Over the last years, they have evolved substantially, giving rise to some of the most powerful methods for optic flow estimation, image segmentation and 3D reconstruction, both in terms of accuracy and in terms of computational speed. In this tutorial I will introduce the basic concepts of variational methods. I will show how problems like image segmentation, stereo and 3D reconstruction can be formulated as variational problems. Subsequently, I will focus on recent developments of convex optimization, convex relaxation and functional lifting which allow to compute globally optimal or near-optimal solutions to respective energy minimization problems. Experimental results demonstrate that these spatially continuous approaches provide numerous advantages over spatially discrete (graph cut) formulations, in particular they are easily parallelized (lower runtime), they require less memory (higher resolution) and they do not suffer from metrication errors (better accuracy).

### Semidefinite Relaxation of Nonconvex Quadratic Optimization: A Key Technique in Signal Processing and Communications

*by Ken Ma and Anthony So*

Semidefinite relaxation (SDR) is an efficient high-performance technique for approximating a class ofchallenging optimization problems, typically in form of nonconvexquadratically constrained quadraticprogram (QCQP). SDR has found numerous applications in signal processing and communications, simplybecause many problems we encounter are naturally, or can be recast as, QCQPs. SDR has been a subject of intense research in both the signal processing and optimization communities, where many powerfulresults, either as encouraging empirical findings or as theoretically profound analyses, have been reported.The significance of SDR is not just in providing a solution approximation tool, but also in fundamentalunderstanding revealing new insights and implications for key, frontier topics in signal processing. This tutorial aims to give an overview of SDR, from its practical deployment, application scope,theoretically advanced results, to key applications. There are two main themes. The first is techniqueoriented,where we will provide essential concepts in using SDR in practice, and the insights behind, anddescribe theoretically advanced results with an emphasis on interpreting their practical implications. Thesecond is application-oriented, where we will concentrate on three key applicationsâ€”MIMO detection,sensor network localization, and transmitbeamforming. The significance and the forefront advances in each application will be covered.

## Monday Afternoon (15:00 - 18:30)

### Applications of Large Random Matrices to Digital Communications and Statistical Signal Processing

*by Philippe Loubaton, Walid Hachem and Jamal Najim*

The goal is this tutorial is to present recent advances in statistical applications of certain Gaussian large random matrices. The tutorial will be structured into three parts. In the first part, general background material on large random matrices will be presented: behaviour of the empirical eigenvalue distribution using Gaussian tools and the Stieltjes transform approach and characterization of the entries of the resolvent. A special emphasis will be put on random matrices with zero mean and non zero mean random separable correlation structure, as well as on the following important special cases: empirical covariance matrix model and non zero mean uncorrelated model, also called information plus noise model. The second part will be devoted to zero mean and information plus noise spiked models and their applications to detection of sources using large sensor networks. The third part will address applications of large random matrices to subspace method for DOA estimation as well as population estimation.

### Quaternion Signal Processing: Theory and Applications

*by Javier VĂa, Nicolas Le Bihan, Danilo Mandic and Steve Sangwine*

The interest in quaternion signal processing has rapidly increased during the last decade due to its applications, amongothers, in image processing, design of space-time block codes, and modeling of wind profiles. This tutorial introduces the fundamentals of quaternion signal processing and presents, in a unified manner, some recent advances in this area. The intended audience is any person willing to discover the potential of quaternion signal processing, and therefore the tutorial will be as self-contained as possible. Specifically,we will start with a comprehensive introduction to quaternion algebra, which will be complemented by a review of some recent works on the statistical analysis of quaternion random vectors, the quaternion extension of classical signal processing methods such as the Fourier transform, and the adaptive filtering of quaternion signals. The theoretical foundations on all these techniques will be complemented by several application examples, including blind decoding in communication systems, processing of polarized waves, and prediction of wind profiles.

### Electronic Trading and Portfolio Optimization: A Signal Processing Perspective

*by Ali Akansu, Ilya Pollak and Francisco Rubio*

The technological advances in high performance computing and digital signal processing coupled with internetworking and abundance of storage media have made a high impact on the financial industry, transforming it into an IT-centric sector where many signal processing and engineering methods and solutions are widely deployed. This development has created a new multidisciplinary research frontier where experts from various fields including mathematical finance, DSP engineering, and computing collaborate to find solutions to highly challenging financial problems coming from diverse application areas such as risk management, optimal trade scheduling, analysis of financial networks, and valuation of complex derivative securities. This tutorial consists of three parts introducing the essentials of market microstructure, exchanges and electronic trading; the problem of optimal allocation of assets in a portfolio; as well as the fundamentals underlying trading strategies that rely on statistical methods for the identification of probabilistic arbitrage opportunities and for the replication of a market index using a sparse basket of securities.

### Omnidirectional Imaging/Image Processing on Manifolds with Applications

*by Pascal Frossard and Ivana Tosic*

The development of image sensors with non-classical geometries, such as fish eye lenses and catadioptric mirror systems has created an essential need for image processing methods adapted to these novel sensors. Since images obtained from most omnidirectional cameras can be uniquely mapped to signals defined on the surface of a unit sphere, the spherical manifold becomes particularly attractive. Spherical signals also appear in many other research areas, such as 3D graphics, astrophysics or medical imaging for example. This myriad of applications has accelerated the advance of signal processing theories and techniques for spherical signals, from the Fourier transform on the sphere (i.e., the spherical harmonics transform) to sparse approximation methods on the sphere and graph-based methods that extend to arbitrary manifolds. The goal of this tutorial is to give a comprehensive overview of the theory and applications of signal processing methods on the sphere and on undirected graphs. The first part of the tutorial will cover the representation theory of spherical signals, starting from the basic spherical harmonics transform and going towards more advanced techniques such as wavelets and sparse representations on the sphere. We will also discuss different discretization frameworks for signal processing on particular manifolds with a special attention to graph-based methods. In the second part of the tutorial, we will demonstrate the benefits of these geometry-aware representations in applications such as omnidirectional image and 3D shape compression, super-resolution of spherical images, depth estimation in omnidirectional camera networks, optical flow estimation in mobile omnidirectional sensors and feature matching in omnidirectional images.

Tutorial Chairs:

- Daniel P. Palomar (palomar@ust.hk)
- Beatrice Pesquet-Popescu (pesquet@tsi.enst.fr)