L2/3 regularization: Convergence of iterative thresholding algorithm
•Under some condition, the sequence generated by the L2/3 algorithm converges to a local minimizer of L2/3 regularization.•Under the same conditions, the asymptotical convergence rate of L2/3 algorithm is linear.•Numerical experiments support our theoretical analysis. The L2/3 regularization is a no...
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| Published in: | Journal of visual communication and image representation Vol. 33; pp. 350 - 357 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Elsevier Inc
01.11.2015
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| ISSN: | 1047-3203, 1095-9076 |
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| Abstract | •Under some condition, the sequence generated by the L2/3 algorithm converges to a local minimizer of L2/3 regularization.•Under the same conditions, the asymptotical convergence rate of L2/3 algorithm is linear.•Numerical experiments support our theoretical analysis.
The L2/3 regularization is a nonconvex and nonsmooth optimization problem. Cao et al. (2013) investigated that the L2/3 regularization is more effective in imaging deconvolution. The convergence issue of the iterative thresholding algorithm of L2/3 regularization problem (the L2/3 algorithm) hasn’t been addressed in Cao et al. (2013). In this paper, we study the convergence of the L2/3 algorithm. As the main result, we show that under certain conditions, the sequence {x(n)} generated by the L2/3 algorithm converges to a local minimizer of L2/3 regularization, and its asymptotical convergence rate is linear. We provide a set of experiments to verify our theoretical assertions and show the performance of the algorithm on sparse signal recovery. The established results provide a theoretical guarantee for a wide range of applications of the algorithm. |
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| AbstractList | •Under some condition, the sequence generated by the L2/3 algorithm converges to a local minimizer of L2/3 regularization.•Under the same conditions, the asymptotical convergence rate of L2/3 algorithm is linear.•Numerical experiments support our theoretical analysis.
The L2/3 regularization is a nonconvex and nonsmooth optimization problem. Cao et al. (2013) investigated that the L2/3 regularization is more effective in imaging deconvolution. The convergence issue of the iterative thresholding algorithm of L2/3 regularization problem (the L2/3 algorithm) hasn’t been addressed in Cao et al. (2013). In this paper, we study the convergence of the L2/3 algorithm. As the main result, we show that under certain conditions, the sequence {x(n)} generated by the L2/3 algorithm converges to a local minimizer of L2/3 regularization, and its asymptotical convergence rate is linear. We provide a set of experiments to verify our theoretical assertions and show the performance of the algorithm on sparse signal recovery. The established results provide a theoretical guarantee for a wide range of applications of the algorithm. |
| Author | Ye, Wanzhou Zhang, Yong |
| Author_xml | – sequence: 1 givenname: Yong surname: Zhang fullname: Zhang, Yong email: 13820161@shu.edu.cn – sequence: 2 givenname: Wanzhou surname: Ye fullname: Ye, Wanzhou email: wzhy@shu.edu.cn |
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| ContentType | Journal Article |
| Copyright | 2015 Elsevier Inc. |
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| DOI | 10.1016/j.jvcir.2015.10.007 |
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| Keywords | L2/3 regularization Local minimizer Iterative thresholding algorithm L1/2 regularization Thresholding formula Sparse signal recovery Asymptotical convergence rate Convergence |
| Language | English |
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| SubjectTerms | [formula omitted] regularization Asymptotical convergence rate Convergence Iterative thresholding algorithm Local minimizer Sparse signal recovery Thresholding formula |
| Title | L2/3 regularization: Convergence of iterative thresholding algorithm |
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