The Convex Relaxation Method on Deconvolution Model with Multiplicative Noise

Abstract

In this paper, we consider variational approaches to handle the multiplicative noise removal and deblurring problem. Based on rather reasonable physical blurring-noisy assumptions, we derive a new variational model for this issue. After the study of the basic properties, we propose to approximate it by a convex relaxation model which is a balance between the previous non-convex model and a convex model. The relaxed model is solved by an alternating minimization approach. Numerical examples are presented to illustrate the effectiveness and efficiency of the proposed method.