A new preconditioning algorithm for finding a zero of the sum of two monotone operators and its application to image restoration problems
Finding a zero of the sum of two monotone operators is one of the most important problems in monotone operator theory, and the forward-backward algorithm is the most prominent approach for solving this type of problem. The aim of this paper is to present a new preconditioning forward-backward algori...
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| Published in: | International journal of computer mathematics Vol. 99; no. 12; pp. 2482 - 2498 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Abingdon
Taylor & Francis
02.12.2022
Taylor & Francis Ltd |
| Subjects: | |
| ISSN: | 0020-7160, 1029-0265 |
| Online Access: | Get full text |
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| Summary: | Finding a zero of the sum of two monotone operators is one of the most important problems in monotone operator theory, and the forward-backward algorithm is the most prominent approach for solving this type of problem. The aim of this paper is to present a new preconditioning forward-backward algorithm to obtain the zero of the sum of two operators in which one is maximal monoton and the other one is M-cocoercive, where M is a linear bounded operator. Furthermore, the strong convergence of the proposed algorithm, which is a broader variant of previously known algorithms, has been proven in Hilbert spaces. We also use our algorithm to tackle the convex minimization problem and show that it outperforms existing algorithms. Finally, we discuss several image restoration applications. |
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| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0020-7160 1029-0265 |
| DOI: | 10.1080/00207160.2022.2068146 |