Preconditioned Three-Operator Splitting Algorithm with Applications to Image Restoration

In this paper, we present primal-dual splitting algorithms for the convex minimization problem involving smooth functions with Lipschitzian gradient, finite sum of nonsmooth proximable functions, and linear composite functions. Many total variation-based image processing problems are special cases o...

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Bibliographic Details
Published in:Journal of scientific computing Vol. 92; no. 3; p. 106
Main Authors: Tang, Yuchao, Wen, Meng, Zeng, Tieyong
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2022
Springer Nature B.V
Subjects:
Algorithms
Composite functions
Computational Mathematics and Numerical Analysis
Convex analysis
Image processing
Image restoration
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Optimization
Splitting
Theoretical
Convex minimization
Three-operator splitting algorithm
Primal-dual algorithm
90C46
90C25
Total variation
47A52
ISSN:0885-7474, 1573-7691
Online Access:Get full text
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Summary:In this paper, we present primal-dual splitting algorithms for the convex minimization problem involving smooth functions with Lipschitzian gradient, finite sum of nonsmooth proximable functions, and linear composite functions. Many total variation-based image processing problems are special cases of such problems. The obtained primal-dual splitting algorithms are derived from a preconditioned three-operator splitting algorithm applied to primal-dual optimality conditions in a proper product space. The convergence of the proposed algorithms under appropriate assumptions on the parameters has been proved. Numerical experiments on a novel image restoration problem are presented to demonstrate the efficiency and effectiveness of the proposed algorithms.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-022-01958-w