A nonlinear multigrid solver with line gauss-seidel-semismooth-newton smoother for the fenchel pre-dual in total variation based image restoration

摘要

Based on the Fenchel pre-dual of the total variation model, a nonlinear multigrid algorithm for image denoising is proposed. Due to the structure of the difierential operator involved in the Euler-Lagrange equations of the dual models, line Gauss-Seidel-semismooth-Newton step is utilized as the smoother, which provides rather good smoothing rates. The paper ends with a report on numerical results and a comparison with a very recent nonlinear multigrid solver based on Chambolle's iteration.