An accelerated homotopy perturbation iteration for nonlinear ill-posed problems in Banach spaces with uniformly convex penalty

Abstract

We propose and analyze an accelerated homotopy perturbation iteration based on Nesterov strategy for nonlinear inverse problems in Banach spaces. The method allows to use L 1-like and total variation-like penalty terms. Therefore, it can cope with the situation where the sought solution is sparse and piece-wise constant. Under some standard assumptions, we show the convergence and regularization properties of the method. Numerical experiments are presented to show the effectiveness as well as the acceleration effect of the proposed method.