A new preconditioning algorithm for finding a zero of the sum of two monotone operators and its application to image restoration problems

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.

KEYWORDS:

• Image restoration problem
• preconditioning forward-backward splitting algorithm
• monotone inclusion problem
• convex minimizaiton problem
• Hilbert space

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 47H05
• 47H10
• 47J25
• 68U10
• 6W258

Disclosure statement

No potential conflict of interest was reported by the author(s).