Simultaneous sparse approximation : insights and algorithms

Alain Rakotomamonjy (1)

1 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes

This paper addresses the problem of simultaneous sparse approximation of signals given an overcomplete dictionary of elementary functions. At first, we propose a simple algorithm for solving the multiple signals extension of the Basis Pursuit Denoising problem. Then, we consider the M-FOCUSS problem which performs sparse approximation by using non-convex sparsity-inducing penalties and show that M-FOCUSS is actually equivalent to an automatic relevance determination problem. Based on this novel insight, we introduce an iterative reweighted Multiple-Basis Pursuit for solving M-FOCUSS; we trade the non-convexity of M-FOCUSS against several resolutions of the convex M-BP problem. Relations between our reweighted algorithm and the Multiple-Sparse Bayesian Learning are also highlighted. Experimental results show how our algorithms behave and how they compare to previous approaches for solving simultaneous sparse approximation problem.

Domaines: Autres [stat.ML]

Alain Rakotomamonjy. Simultaneous sparse approximation : insights and algorithms. 2008. ⟨hal-00328185v1⟩