Research On Image Restoration Problem Based On High-order Affine Total-variation Model

Due to the interference of outside factors,in the process of generation,transmission and storage,the quality of image declines,and then it affects segmentation,reconstruction,fusion,recognition and other follow-up processing quality.Therefore,studying the problem of image restoration and establishing an efficient numerical algorithm has an important theoretical significance and application value in image processing field.Image restoration is a classical ill-conditioned problem,but based on the variation energy functional model,it can not only couple the prior information of image part and overcome ill-conditioning,but also establish an efficient numerical algorithm on the basis of the model's good mathematical properties.Therefore,it received a wide attention in image restoration field.Based on the restoration model of high order total variation,this thesis puts forward a higher-order restoration model which has affine properties and convexity,and establishes an efficient and stable numerical algorithm.Its specific research content is as follows:(1)Based on the total variation(TV-?2),it can keep the image border,and the higherorder total variation(HOTV-?2)model can keep the features of image smooth region.This thesis puts forward a variation model of coupling image gradient information under the ?1norm significance.Because the model has a high order,anisotropic and affine,it can effectively restore the image's affine structure.(2)In order to overcome the numerical difficulties caused by non-smoothness in the modeling process,this thesis uses the duality theory to convert the problem into a problem of saddle point,and it solves the problem based on the classic primitive duality method.At the same time,it analyzes the mathematical properties of the model and algorithm in theory.The numerical comparison verifies the effectiveness of the model and algorithm.