Image Restoration Based On Total Variation Regularization

As a challenging problem in the field of image processing,image restoration is a typical ill-posed inverse problem.It aims to reconstruct the original high quality image from its degraded observed version.In order to cope with the ill-posed nature of image restoration,regularization-based framework was derived.Total variation regularization demonstrates high effectiveness in preserving edges and recovering smooth regions.This paper mainly focuses on the studies of the total variation regularization and its optimal solution.Meanwhile two new image restoration models are proposed based on the edge detection and the nonlocal self-similarity.The detailed content are as follows:In view of the poor performance of traditional total variation model,we proposed a new edge preserving image restoration model by combing weighted total variation and nonlocal regularization.First,this paper proposed a weighted TV model based on edge detection.To take advantage of edge information in images,the proposed method alternatively performed image restoration and edge detection in a way that each benefits from the latest solution of the other.Then we got a new weighted TV model.In order to preferably preserve details and texture,a nonlocal regularization strategy was introduced to the weighted TV model.Finally a modified alternating direction method was used to obtain the optimal solution of the proposed model.Nonetheless,the traditional nonlocal self-similarity regularization which depends on the weighted graph may give rise to disturbance and inaccuracy.To overcome these drawbacks,this paper proposed a nonlocal self-similarity in transform domain.This paper mathematically characterized the nonlocal self-similarity for natural images by means of the distributions of the transform coefficients,which were achieved by transforming the 3D array generated by stacking similar image patches.Then this paper proposed a joint image restoration model,which combined weighted TV and nonlocal self-similarity in transform domain.The proposed model could overcome staircase effect and preserve more edges and details.