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Algorithms for Multiple Basis Pursuit Denoising

Abstract : We address the problem of learning a joint sparse approximation of several signals over a dictionary. We pose the problem as a matrix approximation problem with a row-sparsity inducing penalization on the coefficient matrix. We propose a simple algorithm based on iterative shrinking for solving the problem. At the present time, such a problem is solved either by using a Second-Order Cone programming or by means of a MFocuss algorithm. While the former algorithm is computationally expensive, the latter is efficient but present some pitfalls like presences of fixed points which are undesiderable when solving a convex problem. By analyzing the optimality conditions of the problem, we derive a simple algorithm. The algorithm we propose is efficient and is guaranteed to converge to the optimal solution, up to a given tolerance. Furthermore, by means of a reweighte
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https://hal.inria.fr/inria-00369535
Contributor : Ist Rennes <>
Submitted on : Friday, March 20, 2009 - 11:29:16 AM
Last modification on : Friday, November 1, 2019 - 4:46:06 PM
Long-term archiving on: : Thursday, June 10, 2010 - 5:36:13 PM

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  • HAL Id : inria-00369535, version 1

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Alain Rakotomamonjy. Algorithms for Multiple Basis Pursuit Denoising. SPARS'09 - Signal Processing with Adaptive Sparse Structured Representations, Inria Rennes - Bretagne Atlantique, Apr 2009, Saint Malo, France. ⟨inria-00369535⟩

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