Restoring Multiplicative Noise Image Via The L~0 Quasi-norm Penalization Based On The Total Variation Model

In the process of practical application,there is a widespread multiplicative noise in the laser image,the synthetic aperture radar image,the microscopic image and the medical image.Comparing the image denoising problem with additive noise,the multiplicative noise has a relatively lower uniformity,its fluctuation is more intense,and it has a high influence on the image,so it is relatively trouble to be restored.Therefore the study of restoring image multiplicative noise problem is very important.This dissertation propose a new model based on the total variation with convexity by employing the L~0quasi-norm penalty and then propose a new numerical algorithm to solve the proposed scheme.The main contents are listed below:In chapter 1,we mainly introduce the research backgrounds of image processing and image denoising.We also present some current research stations and then elaborate the main work and structures of this paper.In chapter 2,we give some preliminary knowledge such as some definitions,the PADMM algorithm,the Newton's method,the quantitative standards and the Symbolic notations,et al.In chapter 3,we propose a new method of punishment based on the total variation with convexity.By the operator splitting method,we transform the original problem into a constrained optimization problem,and then solve the constrained optimization problem by using the proximal alternating direction multipliers method(PADMM)in the framework of the augmented Lagrangian strategy.Different to the traditional L2-norm penalty constraint,we use L~0quasi-norm in order to keep the penalty to be more robust.Finally some numerical comparisons verify the validity of the proposed model.Chapter 4 summarizes the main works in this dissertation and point out the future research direction.