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Iterative Methods for Computing the Resolvent of the Sum of a Maximal Monotone Operator and Composite Operator with Applications
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-19, 19 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-05-05
Country of Publication
Egypt
No. of Pages
19
Main Subjects
Abstract EN
Total variation image denoising models have received considerable attention in the last two decades.
To solve constrained total variation image denoising problems, we utilize the computation of a resolvent operator, which consists of a maximal monotone operator and a composite operator.
More precisely, the composite operator consists of a maximal monotone operator and a bounded linear operator.
Based on recent work, in this paper we propose a fixed-point approach for computing this resolvent operator.
Under mild conditions on the iterative parameters, we prove strong convergence of the iterative sequence, which is based on the classical Krasnoselskii–Mann algorithm in general Hilbert spaces.
As a direct application, we obtain an effective iterative algorithm for solving the proximity operator of the sum of two convex functions, one of which is the composition of a convex function with a linear transformation.
Numerical experiments on image denoising are presented to illustrate the efficiency and effectiveness of the proposed iterative algorithm.
In particular, we report the numerical results for the proposed algorithm with different step sizes and relaxation parameters.
American Psychological Association (APA)
Chen, Bao& Tang, Yuchao. 2019. Iterative Methods for Computing the Resolvent of the Sum of a Maximal Monotone Operator and Composite Operator with Applications. Mathematical Problems in Engineering،Vol. 2019, no. 2019, pp.1-19.
https://search.emarefa.net/detail/BIM-1196961
Modern Language Association (MLA)
Chen, Bao& Tang, Yuchao. Iterative Methods for Computing the Resolvent of the Sum of a Maximal Monotone Operator and Composite Operator with Applications. Mathematical Problems in Engineering No. 2019 (2019), pp.1-19.
https://search.emarefa.net/detail/BIM-1196961
American Medical Association (AMA)
Chen, Bao& Tang, Yuchao. Iterative Methods for Computing the Resolvent of the Sum of a Maximal Monotone Operator and Composite Operator with Applications. Mathematical Problems in Engineering. 2019. Vol. 2019, no. 2019, pp.1-19.
https://search.emarefa.net/detail/BIM-1196961
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1196961