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A thresholding algorithm for sparse recovery via Laplace norm

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Abstract

The last decade has witnessed rapidly growing interest in the studies of compressed sensing. \(\ell _{p}\) norm, an approximation to \(\ell _{0}\) norm, can be used to recover a sparse signal from underdetermined linear systems. In comparison with \(\ell _{p}\) norm, another approximation called Laplace norm is a closer approximation to \(\ell _{0}\) norm. The thresholding algorithm is a simple and efficient iterative process to solve the regularization problem. In this paper, we derive the thresholding point and a quasi-analytic thresholding representation for the Laplace regularization, and then a thresholding algorithm for the Laplace regularization is proposed. The numerical results show that the proposed algorithm has higher recovery rate than the \(\ell _{p}\) thresholding algorithms. This thresholding representation can be easily incorporated into the iterative thresholding framework to provide a tool for sparsity problems.

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Acknowledgements

This work is partially supported by the National Natural Science Foundation of China under Grants 61271012 and 61671004.

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Authors and Affiliations

  1. School of Science, Tianjin University of Commerce, Tianjin, China

    Qian Wang

  2. School of Science, Beijing Jiaotong University, Beijing, China

    Qian Wang, Gangrong Qu & Guanghui Han

  3. Beijing Center for Mathematics and Information Interdisciplinary Sciences (BCMIIS), Beijing, China

    Gangrong Qu

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  1. Qian Wang
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  2. Gangrong Qu
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  3. Guanghui Han
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Correspondence to Gangrong Qu.

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Wang, Q., Qu, G. & Han, G. A thresholding algorithm for sparse recovery via Laplace norm. SIViP 13, 389–395 (2019). https://doi.org/10.1007/s11760-018-1367-9

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  • DOI: https://doi.org/10.1007/s11760-018-1367-9

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