An inexact proximal MM method for a class of nonconvex composite image reconstruction models

This paper concerns a class of composite image reconstruction models for impluse noise removal, which is rather general and covers existing convex and nonconvex models proposed for reconstructing images with impluse noise. For this nonconvex and nonsmooth optimization problem, we propose a proximal majorization-minimization (MM) algorithm with an implementable inexactness criterion by seeking in each step an inexact minimizer of a strongly convex majorization of the objective function, and establish the convergence of the iterate sequence under the KL assumption on the constructed potential function. This inexact proximal MM method is applied to handle gray image deblurring and color image inpainting problems, for which the associated potential function satisfy the required KL assumption. Numerical comparisons with two state-of-art solvers for image deblurring and inpainting tasks validate the efficiency of the proposed algorithm and models.