Proximal methods for reweighted lQ-regularization of sparse signal recovery

Bo Peng and Hong-Kun Xu

Applied Mathematics and Computation, 2020, vol. 386, issue C

Abstract: To recover a sparse signal from a noised linear measurement system Ax=b+e, convex lp regularization methods (i.e., 1 ≤ p < 2, in particular, p=1) are commonly used under certain conditions. Recently, however, more attentions have been paid to nonconvex lq regularization methods (i.e., 0 < q < 1, in particular, q=1/2) for recovering a sparse signal. In this paper, we use proximal methods to study both convex and nonconvex reweighted lQ regularization for recovering a sparse signal. Convex lQ regularization is introduced by S. Voronin and I. Daubechies [19]. We extend it to the nonconvex case and our results therefore supplement those of Voronin and Daubechies [19]. We also study Nesterov’s acceleration method for the nonconvex case. Our numerical experiments show that nonconvex lQ regularization can more effectively recover sparse signals.

Keywords: Proximal method; Sparsity; Noise; Signal recovery; lQ-Regularization; Reweight; Nonconvex optimization (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320303702

DOI: 10.1016/j.amc.2020.125408

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