Convex regularized inverse filtering methods for blind image deconvolution

In this paper, we study a regularized inverse filtering method for blind image deconvolution. The main idea is to make use of nonnegativity and support constraints, and to incorporate regularization terms to establish a convex programming model which aims to determine an inverse filter for image deconvolution. Because of the convexity of the proposed energy functional, the existence of the solution can be guaranteed. We employ the alternating direction method of multipliers to solve the resulting optimization problem. In this paper, we consider three possible regularization methods in the inverse filtering, namely total variation, nonlocal total variation, and framelet approaches. Experimental results of these regularization methods are reported to show that the performance of the proposed methods is better than the other testing methods for several testing images.