Priori-based Image Restoration Via Weighted Schatten-p Norm Minimization

Image restoration is a hot research direction in the field of image processing,how to restore images damaged by noise or with data missing has been a topic of wide concern.In recent years,image restoration algorithms based on low-rank matrix reconstruction have been proposed and demonstrated their excellent performance.Low-rank prior has become a kind of prior knowledge with high utilization rate in image restoration algorithms.Since a better image restoration method also reveals a better prior knowledge of natural images,it is very important to explore and make good use of the prior information.Based on low-rank priori,this thesis studies the problem of image denoising and matrix completion which utilize two prior information simultaneously.The main contents of this thesis are as follows:In the first chapter,the background and significance of image restoration are briefly introduced.Then,the research status of image denoising and matrix completion is summarized.Finally,the main research contents and organizational structure of this thesis are explained.In the second chapter,the basic theory of low-rank matrix restoration is given,including low-rank matrix approximation theory and matrix rank minimization theory.Finally,the alternating direction method of multipliers used to solve optimization problems in this thesis is briefly introduced.In the third chapter,for the image damaged by impulse noise,the low-rank matrix approximation method is used to propose the impulse noise removal model,and the model is based on the combination of image low-rank and noise prior information.An efficient optimization algorithm is proposed by using the framework of alternating direction method of multipliers to solve the proposed non-convex optimization problem.The comparison between the proposed algorithm and many excellent impulse noise removal algorithms on real image data shows that the proposed algorithm has great improvement in visual effect and PSNR value.In the fourth chapter,the problem of matrix completion based on low-rank and smooth priors is studied.Based on the rank minimization theory of the matrix,in the nuclear norm minimization matrix completion algorithm,aiming at the problem that the nuclear norm is not the best approximation function of the rank function,this thesis combined the advantages of weighted Schatten-p norm and truncated nuclear norm,and adopted weighted truncated Schatten-p norm as the approximation function of the rank function.At the same time,the improved second-order total variational norm is used to model the local smooth prior information of the image,and a WTP-MSTVM matrix completion model is proposed.Similarly,an efficient optimization algorithm based on the framework of alternating direction method of multipliers is proposed to solve the proposed optimization problem.Finally,a large number of numerical experiments verify that the image restoration effect of the proposed algorithm has been significantly improved compared with the existing methods.Chapter five summarizes the works of this thesis,and analyzes and looks forward to the future research direction of this thesis.