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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https://hal.inria.fr/inria-00130123
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Submitted on : Friday, June 22, 2007 - 2:47:55 PM
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Lasse Borup, Rémi Gribonval, Morten Nielsen. Beyond coherence : recovering structured time-frequency representations. [Research Report] PI 1833, 2007, pp.13. ⟨inria-00130123v2⟩

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