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A fast proximal point algorithm for ℓ1-minimization problem in compressed sensing

Author

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  • Zhu, Yun
  • Wu, Jian
  • Yu, Gaohang

Abstract

In this paper, a fast proximal point algorithm (PPA) is proposed for solving ℓ1-minimization problem arising from compressed sensing. The proposed algorithm can be regarded as a new adaptive version of customized proximal point algorithm, which is based on a novel decomposition for the given nonsymmetric proximal matrix M. Since the proposed method is also a special case of the PPA-based contraction method, its global convergence can be established using the framework of a contraction method. Numerical results illustrate that the proposed algorithm outperforms some existing proximal point algorithms for sparse signal reconstruction.

Suggested Citation

  • Zhu, Yun & Wu, Jian & Yu, Gaohang, 2015. "A fast proximal point algorithm for ℓ1-minimization problem in compressed sensing," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 777-784.
    • Handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:777-784
    DOI: 10.1016/j.amc.2015.08.082
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    References listed on IDEAS

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    1. B. S. He & X. L. Fu & Z. K. Jiang, 2009. "Proximal-Point Algorithm Using a Linear Proximal Term," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 299-319, May.
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