A convergence analysis for iterative sparsification projection with soft-thresholding.

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Author: Tao Zhu
Date: Nov. 2021
From: Signal, Image and Video Processing(Vol. 15, Issue 8)
Publisher: Springer
Document Type: Report; Brief article
Length: 229 words

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Abstract :

Keywords: Convergence; Iterative sparsification projection; Fixed point mapping Abstract The recently proposed iterative sparsification projection (ISP), a fast and robust sparse signal recovery algorithm framework, can be classified as smooth-ISP and nonsmooth-ISP. However, no convergence analysis has been established for the nonsmooth-ISP in the previous works. Motivated by this absence, the present paper provides a convergence analysis for ISP with soft-thresholding (ISP-soft) which is an instance of the nonsmooth-ISP. In our analysis, the composite operator of soft-thresholding and proximal projection is viewed as a fixed point mapping, whose nonexpansiveness plays a key role. Specifically, our convergence analysis for the sequence generated by ISP-soft can be summarized as follows: 1) For each inner loop, we prove that the sequence has a unique accumulation point which is a fixed point, and show that it is a Cauchy sequence 2) for the last inner loop, we prove that the accumulation point of the sequence is a critical point of the objective function if the final value of the threshold satisfies a condition, and show that the corresponding objective values are monotonically nonincreasing. A numerical experiment is given to validate some of our results and intuitively present the convergence. Author Affiliation: (1) School of Electronic and Information Engineering, South China University of Technology, 510640, Guangzhou, China (a) ee_zt_21@mail.scut.edu.cn Article History: Registration Date: 04/08/2021 Received Date: 04/11/2020 Accepted Date: 04/08/2021 Online Date: 04/23/2021 Byline:

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Gale Document Number: GALE|A678453285