Fast Algorithms for the Anisotropic LLT Model in Image Denoising

Abstract

In this paper, we propose a new projection method for solving a general minimization problems with two $L^1$-regularization terms for image denoising. It is related to the split Bregman method, but it avoids solving PDEs in the iteration. We employ the fast iterative shrinkage-thresholding algorithm (FISTA) to speed up the proposed method to a convergence rate $O$($k^-$$^2$). We also show the convergence of the algorithms. Finally, we apply the methods to the anisotropic Lysaker, Lundervold and Tai (LLT) model and demonstrate their efficiency.