A Modified Inertial Viscosity Algorithm for an Infinite Family of Nonexpansive Mappings and Its Application to Image Restoration

Abstract

. The image restoration problem is one of the popular topics in image processing studied by many authors because of its applications in various areas. This paper aims to present a new algorithm using viscosity approximation with inertial effect to find a common fixed point of an infinite family of nonexpansive mappings in a Hilbert space and obtain more quality images from degenerate images. Some strong convergence theorems are proved under mild conditions. The obtained results are applied to solve monotone inclusion problems, convex minimization problems, variational inequality problems, and generalized equilibrium problems. It is shown that the proposed algorithm performs better than some other algorithms. Also, the effects of inertial and viscosity terms in the algorithm on image restoration are investigated.