A Class Of Total Generalized Variation Based Methods On Image Denoising And Restoration

In the process of imaging,storage and transmission,due to the influence of a variety of factors,the image often contains noise and even appears blur.The noisy or blurring image often loses important information contained in the original image,which will be quite different from the original image.However,in order to meet the needs of actual production and life,we need the clear image.Therefore,the research on image denoising and restoration method is of great significance.Total variation based methods for image denoising and restoration have always been a hot topic at home and abroad.In this paper,we mainly study the second-order total generalized variation based methods for image denoising and restoration.The main results are listed as follows.Firstly,a method which combines the shearlet transform and the second-order total generalized variation is proposed for solving Cauchy image denoising problem.By using the dual technique of optimization,this problem is transformed into a minimax problem,then the Chambolle and Pock's first-order primal-dual algorithm is used to solve this minimax problem.Furthermore,the proposed method is compared with some existing state-of-the-art methods.Secondly,the Morozov's discrepancy principle is used to choose the regularization parameter of the second-order total generalized variation Gaussian image restoration model.By combining with the dual form of the second-order total generalized variation,the original problem is transformed into a minimax problem,then the transformed Chambolle and Pock's first-order primal-dual algorithm is used to solve the primal problem.Numerical experimental results demonstrate that the proposed method can obtain the better image restoration results,compared with other existing methods.Thirdly,to further enhance the image denoising effect,a box constrained total generalized variation method is proposed by simply projecting all pixel values of the denoised image to lie in a certain interval.Similarly,by combining with the dual form of the second-order total generalized variation,the original problem is transformed into a minimax problem,then the Chambolle and Pock's first-order primal-dual algorithm is used to solve this minimax problem.At last,numerical experimental results demonstrate the effectiveness of our proposed method for the Poissonian image denoising problem.