Multiplicative Noise Removal Based On Split-Bregman Algorithm

Noise removal is one of the fundamental tasks of image restoration which can get clear images from the corrupted ones by different noises. The researches on variational models of additive noise removal are successful, but the investigation of multiplicative noise removal is late. The variational models for multiplicative noise reduction are deeply discussed in this paper, and some solutions to existing problems are put forward. And several aspects are introduced as follows:Firstly, Split-Bregmen algorithm transforms original variational models into solutions of simple Poisson equations and generalized soft thresholding formulas by introducing auxiliary variables. In this way, the calculation speed of variational models is improved. Moreover, Bregman iteration speeds up the convergence rate of energy functional and enhances restoration quality. Secondly, a general variational model for different cases of multiplicative noise removal is proposed, which includes a data term and a regularization term. The data term can be derived from Gauss, Rayleigh, Gamma, Poisson distribution of noises, the regularization term can be TV (Total Variation). PM (Perona and Malik) and Charbonnier regulerizers. The model is tested through numerical experiments on different combinations of data terms and regularization terms. Thirdly, TV model of grayscale images is extended to color images based on analysis of principles that color image noise reduction should follow. A general model for multiplicative noise removal of color images and related Split-Bregman algorithm is designed. Some experiments on color images corrupted by additive and multiplicative noise are implemented to verify the effectiveness of Split-Bregman methods.