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Beyond coherence : recovering structured time-frequency representations

Lasse Borup 1 Rémi Gribonval 2 Morten Nielsen 1 
2 METISS - Speech and sound data modeling and processing
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : We consider the problem of recovering a structured sparse representation of a signal in an overcomplete time-frequency dictionary with a particular structure. For infinite dictionaries that are the union of a nice wavelet basis and a Wilson basis, sufficient conditions are given for the Basis Pursuit and (Orthogonal) Matching Pursuit algorithms to recover a structured representation of an admissible signal. The sufficient conditions take into account the structure of the wavelet/Wilson dictionary and allow very large (even infinite) support sets to be recovered even though the dictionary is highly coherent.
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Lasse Borup, Rémi Gribonval, Morten Nielsen. Beyond coherence : recovering structured time-frequency representations. Applied and Computational Harmonic Analysis, Elsevier, 2008, 24 (1), pp.120-128. ⟨10.1016/j.acha.2007.09.002⟩. ⟨inria-00544766⟩

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