An inertial-type method for solving image restoration problems.

We first establish weak convergence results regarding an inertial Krasnosel'skiĭ-Mann iterative method for approximating common fixed points of countable families of nonexpansive mappings in real Hilbert spaces with no extra assumptions on the considered countable families of nonexpansive mappings. The method of proof and the imposed conditions on the iterative parameters are different from those already available in the literature. We then present some applications to the Douglas–Rachford splitting method and image restoration problems, and compare the performance of our method with that of other popular inertial Krasnosel'skiĭ-Mann methods which can be found in the literature. [ABSTRACT FROM AUTHOR]