An iterative decoupled method with weighted nuclear norm minimization for image restoration

Recently, iterative methods based on decoupling of deblurring and denoising steps have received remarkable attention in image processing problems. In this paper, we propose an effective iterative decoupled approach for image restoration. The main idea is to split the image restoration problem into two minimization subproblems: deblurring and denoising. An efficient deblurring method using fast transforms is used in the deblurring step and a weighted nuclear norm minimization method is employed in the denoising step. We analyze the convergence of the developed iterative method under some assumptions. Some numerical experiments are given to demonstrate the effectiveness of the proposed method.