A nonconvex l1(l1 - l2) model for image restoration with impulse noise

In this paper, we propose a model for image restoration with blur and impulse noise, it is composed of data fitting term and a nonconvex regularization term, which is the weighted difference of l(1)-norm and l(2)-norm based on wavelet frame. The combined model is difficult to solve by the corresponding Euler Lagrangian equations, here we solve it by alternating direction method of multipliers (ADMM). We describe the detailed process of the algorithm, and establish the convergence of the algorithm. The experimental outcomes on different blurs and different impulse noises demonstrate that the proposed approach is better than those existing methods in terms of standard signal-to-noise ratio (PSNR), relative error (ReErr), and visual quality. (C) 2020 Elsevier B.V. All rights reserved.