Split Bregman Algorithm of TV-L1 Model for Image Diffusion

The TV-L1 model for image diffusion can preserve geometry and reduce the loss of image contrast better than the classical TV-L2 model, but its traditional difference scheme is complex and its computation efficiency is low. The minimization of energy functional of the TV-LI model is transformed to three simple sub-problems by means of introducing two auxiliary variables to reduce complexity, and its computational efficiency is improved by means of shrinkage operator of soft threshold formula and solving the related simple Poisson equations using Gauss-Seidel method. The split Bregman algorithm which combines the Split method and the Bregman iterative regularization method is designed for the TV-L1 model to improve the quality of diffused images. Finally, some numerical experiments validate the methods proposed in this paper.