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Proximal methods for reweighted lQ-regularization of sparse signal recovery

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  • Peng, Bo
  • Xu, Hong-Kun

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.

Suggested Citation

  • Peng, Bo & Xu, Hong-Kun, 2020. "Proximal methods for reweighted lQ-regularization of sparse signal recovery," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    • Handle: RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320303702
    DOI: 10.1016/j.amc.2020.125408
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    1. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    2. Kristian Bredies & Dirk A. Lorenz & Stefan Reiterer, 2015. "Minimization of Non-smooth, Non-convex Functionals by Iterative Thresholding," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 78-112, April.
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    Cited by:

    1. Yue, Yuanyuan & Liu, Qingshan, 2024. "Distributed dual consensus algorithm for time-varying optimization with coupled equality constraint," Applied Mathematics and Computation, Elsevier, vol. 474(C).

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