The Total Variation model of Rudin, Osher, and Fatemi for  image denoising is considered to be one of the best denoising models.  But there were two serious issues about the ROF model. First, it was  very complicated to compute the solutions of the optimization problems  induced by the variational method. Second, it was difficult to extract  textures from images by using the ROF model. For the first issue,  Goldstein and Osher recently introduced the split Bregman method for  L1 regularized problems. The Bregman method gave rise to very  efficient algorithms for solutions of the ROF model. In this talk, we  will give a rigorous proof for the convergence of the Bregman method.  For the second issue, we will propose some new algorithms based on the  combination of the Bregman method with wavelet packet decompositions.  It will be demonstrated that our algorithms have better performance in  texture preservation.