A symmetric alternating minimization algorithm for total variation minimization

•We propose a symmetric alternation minimization (AM) algorithm, which takes the special x¯k→zk→xk (sGS) iterative scheme rather than the usual Gauss-Seidel zk → xk iterative scheme, for solving the TV regularization problem.•We show that the proposed algorithm is equivalent to the accelerated proxi...

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Bibliographic Details
Published in:Signal processing Vol. 176; p. 107673
Main Authors: Lei, Yuan, Xie, Jiaxin
Format: Journal Article
Language:English
Published: Elsevier B.V 01.11.2020
Subjects:
Acceleration
Sparse recovery
Symmetric alternating minimization
Symmetric Gauss-Seidel
Total variation
68U10
90C25
Symmetric Gauss-Seidel
Total variation
Symmetric alternating minimization
Sparse recovery
Acceleration
94A12
ISSN:0165-1684
Online Access:Get full text
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Summary:•We propose a symmetric alternation minimization (AM) algorithm, which takes the special x¯k→zk→xk (sGS) iterative scheme rather than the usual Gauss-Seidel zk → xk iterative scheme, for solving the TV regularization problem.•We show that the proposed algorithm is equivalent to the accelerated proximal gradient (APG) method and prove that the proposed algorithm can obtain the ϵ-optimal solution within O(1/ϵ1.5) iterations.•Numerical examples show the good performance of our proposed algorithm for image denoising, image deblurring, and analysis sparse recovery. In this paper, we propose a novel symmetric alternating minimization algorithm to solve a broad class of total variation (TV) regularization problems. Unlike the usual zk → xk Gauss-Seidel cycle, the proposed algorithm performs the special x¯k→zk→xk cycle. The main idea for our setting is the recent symmetric Gauss-Seidel (sGS) technique which is developed for solving the multi-block convex composite problem. This idea also enables us to build the equivalence between the proposed method and the well-known accelerated proximal gradient (APG) method. The faster convergence rate of the proposed algorithm can be directly obtained from the APG framework and numerical results including image denoising, image deblurring, and analysis sparse recovery problem demonstrate the effectiveness of the new algorithm.
ISSN:0165-1684
DOI:10.1016/j.sigpro.2020.107673