DISCRETE WAVELET FRAMES ON THE SPHERE (TueAmOR2)

Author(s) : Iva Bogdanova (ITS, Swiss Federal Institute of Technology (EPFL), Switzerland) Pierre Vandergheynst (ITS, Swiss Federal Institute of Technology (EPFL), Switzerland) Jean-Pierre Antoine (FYMA, Univ. Cath. Louvain, Belgium) Laurent Jacques (FYMA, Univ. Cath. Louvain, Belgium) Marcela Morvidone (FYMA, Univ. Cath. Louvain, Belgium)

Abstract : In this paper we exploit the Continuous Wavelet Transform (CWT) on the sphere to build the associated Discrete Wavelet Frames. We first explore half-continuous frames, i.e, frames where the position remains a continuous variable, and then move on to a fully discrete theory. This forces us to introduce the notion of controlled frames, which reflects the particular nature of the underlying theory, particularly the apparent conflict between dilation and the compacity of the $Sî2$ manifold. We conclude with some numerical illustrations and future work.

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