Average Case Analysis of Multichannel Thresholding

Rémi Gribonval (1) , Boris Mailhé (1) , Holger Rauhut (2) , Karin Schnass (3) , Pierre Vandergheynst (3)

1 METISS - Speech and sound data modeling and processing
2 Faculty of Mathematics [Vienna]
3 LTS2 - EPFL

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.

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Rémi Gribonval, Boris Mailhé, Holger Rauhut, Karin Schnass, Pierre Vandergheynst. Average Case Analysis of Multichannel Thresholding. Acoustics, Speech and Signal Processing, 2007. ICASSP 2007. IEEE International Conference on, Apr 2007, Honolulu, Hawai, United States. pp.II-853 - II-856, ⟨10.1109/ICASSP.2007.366370⟩. ⟨inria-00544776⟩