An accelerated forward-backward algorithm with applications to image restoration problems

Abstract

In this research, we introduce an accelerated fixed point algorithm for solving a common fixed point of a countable family of nonexpansive operators and analyze convergence behavior of the proposed method. We prove weak convergence of the proposed algorithm under some suitable conditions. We also apply our main result for solving a convex minimization problem. As an application, we apply our main result to solve image restoration problems and compare its convergence behavior with the existing well-known algorithms. We find that our algorithm outperforms than the others in the literature.