A new preconditioning algorithm for finding a zero of the sum of two monotone operators and its application to image restoration problems. Issue 12 (2nd December 2022)

• Record Type: Journal Article
• Authors: Altiparmak, Ebru; Karahan, Ibrahim
• Is Part Of: International journal of computer mathematics. Volume 99:Issue 12(2022)
• Page Start: 2482
• Page End: 2498
• Publication Date: 2022-12-02
• Subjects: Image restoration problem -- preconditioning forward-backward splitting algorithm -- monotone inclusion problem -- convex minimizaiton problem -- Hilbert space; 47H05 -- 47H10 -- 47J25 -- 68U10 -- 6W258; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2022.2068146
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: 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.