Multichannel thresholding with sensing dictionaries

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 shows introduces the use sensing dictionaries for p-thresholding, an algorithm to compute simultaneous sparse approximations of multichannel signals over redundant dictionaries. We do both a worst case and average case recovery analyses of this algorithm and show that the latter results in much weaker conditions on the dictionary, sensing dictionary pair. We then do numerical simulations to confirm our theoretical findings, showing that p-thresholding is an interesting low complexity alternative to simultaneous greedy or convex relaxation algorithms for processing sparse multichannel signals with balanced coefficients, and finally point a connection to compressed sensing exploiting the additional freedom in designing the sensing dictionary.

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. Multichannel thresholding with sensing dictionaries. Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP'07), Dec 2007, St Thomas, Virgin Islands, United States. pp.133 - 136, ⟨10.1109/CAMSAP.2007.4497983⟩. ⟨inria-00544777⟩