Average case analysis of multichannel sparse approximations using <sub><i>p-</i></sub>thresholding

Karin Schnass; Pierre Vandergheynst; Rémi Gribonval; Boris Mailhe; Holger Rauhut

doi:10.1117/12.733073

20 September 2007 Average case analysis of multichannel sparse approximations using p-thresholding

Karin Schnass, Pierre Vandergheynst, Rémi Gribonval, Boris Mailhe, Holger Rauhut

Proceedings Volume 6701, Wavelets XII; 67011X (2007) https://doi.org/10.1117/12.733073
Event: Optical Engineering + Applications, 2007, San Diego, California, United States

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.

Citation Download Citation

Karin Schnass, Pierre Vandergheynst, Rémi Gribonval, Boris Mailhe, and Holger Rauhut "Average case analysis of multichannel sparse approximations using p-thresholding", Proc. SPIE 6701, Wavelets XII, 67011X (20 September 2007); https://doi.org/10.1117/12.733073

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