Recovering sparse signals with a certain family of non-convex penalties and DC programming

Abstract : This paper considers the problem of recovering a sparse signal representation according to a signal dictionary. This problem could be formalized as a penalized least-squares problem in which sparsity is usually induced by a l1 -norm penalty on the coefficients. Such an approach known as the Lasso or Basis Pursuit Denoising has been shown to perform reasonably well in some situations. However, it was also proved that non-convex penalties like the pseudo lq -norm with q < 1 or SCAD penalty are able to recover sparsity in a more efficient way than the Lasso. Several algorithms have been proposed for solving the resulting non-convex least-squares problem. This paper proposes a generic algorithm to address such a sparsity recovery problem for some class of non-convex penalties. Our main contribution is that the proposed methodology is based on an iterative algorithm which solves at each iteration a convex weighted Lasso problem. It relies on the family of non-convex penalties which can be decomposed as a difference of convex functions. This allows us to apply difference of convex functions programming which is a generic and principled way for solving non-smooth and non-convex optimization problem. We also show that several algorithms in the literature dealing with non-convex penalties are particular instances of our algorithm. Experimental results demonstrate the effectiveness of the proposed generic framework compared to existing algorithms, including iterative reweighted least-squares methods.
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https://hal.archives-ouvertes.fr/hal-00439453
Contributor : Alain Rakotomamonjy <>
Submitted on : Monday, December 7, 2009 - 3:40:42 PM
Last modification on : Friday, May 3, 2019 - 9:30:19 AM

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  • HAL Id : hal-00439453, version 1

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Gilles Gasso, Alain Rakotomamonjy, Stephane Canu. Recovering sparse signals with a certain family of non-convex penalties and DC programming. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2009, 57 (12), pp.4686-4698. ⟨hal-00439453⟩

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