Average case analysis of multichannel sparse approximations using p-thresholding

Karin Schnass 1 Pierre Vandergheynst 1 Rémi Gribonval 2 Holger Rauhut 3
2 METISS - Speech and sound data modeling and processing
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : This paper introduces $p$-thresholding, an algorithm to compute simultaneous sparse approximations of multichannel signals over redundant dictionaries. We work out both worst case and average case recovery analyses of this algorithm and show that the latter results in much weaker conditions on the dictionary. Numerical simulations confirm our theoretical findings and show that \$p\$-thresholding is an interesting low complexity alternative to simultaneous greedy or convex relaxation algorithms for processing sparse multichannel signals with balanced coefficients.
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Karin Schnass, Pierre Vandergheynst, Rémi Gribonval, Holger Rauhut. Average case analysis of multichannel sparse approximations using p-thresholding. SPIE Optics and Photonics, Wavelet XII,, Aug 2007, San Diego, California, United States. ⟨10.1117/12.733073⟩. ⟨inria-00544981⟩

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