The Study Of Numerical Method Of Primal Dual Based Image Restoration Model

Ima ge restoration is one of the classic problems in the field of ima ge processing. It is aprocessing field of improve the ima ge appearance. This paper first introduces some basicknowledge of ima ge and ima ge restoration, and ma inly analyses the total variation (TV)based ima ge restoration and its development process.Then in this paper, we introduces a kind of prima l dual method for solving total variation(TV) minimiza tion problems in ima ge restoration. The ma in idea is before apply alineariza tion technique like Newton's method, by introducing an additiona l variable toremove some of the singula rity caused by the nond ifferentiability of the quantity ?u in thedefinition of the TV-norm. The experiment results did by Chan, Golub and Mulet show thatthis method seems to be globa lly convergent. But when dealing with large problems we needlong operation time, therefore, we also present a new block-based image denoising methodwhich is based on the prima l dual method. The numerica l experiments show that this methodcan significa ntly improve the efficiency of denoising. And also have a certain improve in theima ge restoration quality.Finally, this paper introduces a new kind of iterative regularization method for ima gerestoration. It is a iterative regularization procedure for inverse problems based on the use ofgenera lized Bregman dista nces, with particular focus on the problems arising in total variationbased ima ge restoration. We obtain rigorous convergence results and effective stoppingcriterion for the genera l procedure. Specifically, when a discrepa ncy principle is used as thestopping criterion, the error measured by the Bregman dista nce between the restoration ima geand the noise-free ima ge decreases until termination. The numerica l results for denoisingappear to give significant improvement over standard models.