Beyond coherence : recovering structured time-frequency representations

Lasse Borup (1) , Rémi Gribonval (2) , Morten Nielsen (1)

1 Department of Mathematical Sciences [Aalborg]
2 METISS - Speech and sound data modeling and processing

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.

Mots clés: Sparse representation; overcomplete dictionary; matching pursuit; basis pursuit; time-frequency dictionaries; wavelets; Wilson basis; linear programming; greedy algorithm; identifiability; inverse problem

Domaines: Son [cs.SD]

Lasse Borup, Rémi Gribonval, Morten Nielsen. Beyond coherence : recovering structured time-frequency representations. [Research Report] PI 1833, 2007, pp.13. ⟨inria-00130123v2⟩