An Accelerated Fixed-Point Algorithm with an Inertial Technique for a Countable Family of <i>G</i>-Nonexpansive Mappings Applied to Image Recovery

Abstract

Many authors have proposed fixed-point algorithms for obtaining a fixed point of G-nonexpansive mappings without using inertial techniques. To improve convergence behavior, some accelerated fixed-point methods have been introduced. The main aim of this paper is to use a coordinate affine structure to create an accelerated fixed-point algorithm with an inertial technique for a countable family of G-nonexpansive mappings in a Hilbert space with a symmetric directed graph G and prove the weak convergence theorem of the proposed algorithm. As an application, we apply our proposed algorithm to solve image restoration and convex minimization problems. The numerical experiments show that our algorithm is more efficient than FBA, FISTA, Ishikawa iteration, S-iteration, Noor iteration and SP-iteration.

Keywords

• convex minimization
• coordinate affine
• <i>G</i>-nonexpansive
• image restoration problem
• inertial techniques
• weak convergence