A general variational model for multiplicative noise removal and its split Bregman algorithm

The variational models for multiplicative noise removal have been received considerable attention recently. 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 original minimization problem is transformed into solutions of simple Poisson equations and generalized soft thresholding formulas by using split Bregman algorithm, which is designed in this paper based on the general variational model for multiplicative noise removal. The model and algorithm are tested through different combinations of data terms and regularization terms.