| The Rudin-Osher-Fatemi (ROF) total-variation model is one of the most popularand effective models for image denoising. Many efficient methods, including Split-Bregman Methods, Primal-Dual Methods, Gradient Descent Methods and AugmentedLagrangian approaches, have been developed for solving the model. In 2011, Y. Xu etal.[1] proposed a novel framework for solving the ROF model by means of the prox-imity operator. The key steps of the framework consist in first rewritting the originalmodel as a fixed-point formulation and then obtaining the fixed points by a certainfixed point algorithm with fixed weights for nonexpansive operators. In this thesis,based on the previous solution setting, we are going to borrow the Mann style itera-tion algorithm to work out fixed points, instead of the method used in [1], to increasethe efficiency of the iteration method. Through subtly choosing a sequence of weights,which are varied adaptively, we obtain a new-type algorithm for image denoising. Thismethod is convergent theoretically, and performs almost the same as the most efficientalgorithm for image denoising at present, i.e., the PDHG method with particularlychosen parameters [2]. However, there is no convergence results for the latter methodup to now. We provide a series of numerical experiments to show the performanceof our Mann method and to compare it with the PDHG method, from which someobservations are also available. |
