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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Bibliographic Details
Published in:Journal of visual communication and image representation Vol. 33; pp. 350 - 357
Main Authors: Zhang, Yong, Ye, Wanzhou
Format: Journal Article
Language:English
Published: Elsevier Inc 01.11.2015
Subjects:
[formula omitted] regularization
Asymptotical convergence rate
Convergence
Iterative thresholding algorithm
Local minimizer
Sparse signal recovery
Thresholding formula
L2/3 regularization
Local minimizer
Iterative thresholding algorithm
L1/2 regularization
Thresholding formula
Sparse signal recovery
Asymptotical convergence rate
Convergence
ISSN:1047-3203, 1095-9076
Online Access:Get full text
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Summary:•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.
ISSN:1047-3203
1095-9076
DOI:10.1016/j.jvcir.2015.10.007