Research On Removing Salt And Pepper Noise By Total Variation And Low Rank Regularization

Image denoising plays an important role in image processing.As an important pretreatment technology,good denoising directly determines the effectiveness of the follow-up work.In recent years,image denoising using total variation as a priori information has been widely researched.However,this prior information may not be sufficient to restore satisfactory restored image from its incomplete observations,which leads to the failure of restored image in meeting the requirements of subsequent processing.Among many denoising problems,the problem of salt and pepper noise removal is an important research topic.Aiming at the elimination of this kind of noise,the main innovations of this dissertation are as follows:· Since some existing denoising models can not describe the local features of the image well,a new denoising model based on anisotropic total variation and nuclear norm regularization is proposed in this dissertation.In the total variation regularization term,one weighted matrix T to punish the direction of the gradient operator tending to bigger weight is introduced,thus achieving the purpose of effectively depicting the local features of the image.In addition,we also introduce the nuclear norm regularization to describe the low rank properties of the image.· Considering the relationship between the singular value of the image matrix and noise intensity,and the fact that high order total variation can effectively eliminate the step effect,we propose a new denoising model based on high order total variation and nuclear norm regularization.This model not only has the advantage of high order total variation model to maintain the smooth area of the image,but also has the performance of low rank representation model to depict the detail information of the image.So it can effectively keep the detailed information and structure information of restored image.· Since the proposed models are separable and non-smooth convex optimization problems,the classic alternating direction multiplier method is used to solve them,that is,the original problem is transformed into the saddle point problem by introducing some auxiliary variables,and efficient numerical method is used to solve the problems.And the convergence and stability of the numerical algorithm are proved theoretically.Finally,the numerical results show that the proposed models are superior to other representative total variation image to remove salt and pepper noise models in terms of signal-to-noise ratio and structural similarity.