Relaxed Alternating Minimization Algorithm for Separable Convex Programming with Applications to Imaging
Year: 2022
Author: Shuangshuang Wu, Yuchao Tang, Tieyong Zeng
CSIAM Transactions on Applied Mathematics, Vol. 3 (2022), Iss. 4 : pp. 626–661
Abstract
We propose a relaxed alternating minimization algorithm for solving two-block separable convex minimization problems with linear equality constraints, where one block in the objective functions is strongly convex. We prove that the proposed algorithm converges to the optimal primal-dual solution of the original problem. Furthermore, the convergence rates of the proposed algorithm in both ergodic and nonergodic senses have also been studied. We apply the proposed algorithm to solve several composite convex minimization problems arising in image denoising and evaluate the numerical performance of the proposed algorithm on a novel image denoising model. Numerical results for both artificial and real noisy images demonstrate the efficiency and effectiveness of the proposed algorithm.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.SO-2021-0039
CSIAM Transactions on Applied Mathematics, Vol. 3 (2022), Iss. 4 : pp. 626–661
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 36
Keywords: Alternating minimization algorithm strongly convex function total variation image denoising.