Image Restoration Based On Hybrid Data Fidelity With Weighted Total Variation

At present,as the most important carrier of information,digital images have a great impact on people’s daily life more and more widely.The quality of the digital image directly affects people’s visual perception and information acquisition.However,multiple factors result in image degradation in the process of acquisition,transmission and storage.Hence,it is always a central issue in digital image processing to recover potential high quality images from degraded images effectively.In general,the restoration of degraded images is an ill-posed problem.Therefore,the ill-posed image restoration problem is turned into the well-posed problem via constraining solution space with the regularized image prior information.l₂,l₁ and total variation（TV）norm are typical regularization priors and these regularization models are widely used in image restoration.However,the recovery quality and speed of these methods need to be improved.The main content of the paper: Firstly,the paper introduces the research background and significance of image processing.The model and research status of image denoising and image deblurring are also described.Secondly,from the perspective of regularization,the paper researches and analyzes common TV regularization model,the basic mathematical concepts,definitions and commonly used algorithms are given.Thirdly,the paper proposes a novel hybrid data fidelity with weighted TV model.In addition,the difference of convex（DCA）with the Split Bregman Iteration（SBI）and the difference of convex（DCA）with the augmented Lagrangian method（ALM）algorithms are proposed,and the convergence of the algorithms is analyzed.Finally,the experimental section verifies the rationality of the algorithm.The main innovations of the paper include three aspects.Firstly,based on two types of image restoration models discussed above,we propose a hybrid data fidelity term with weighted TV model.The regularization prior of the proposed model is weighted TV,which approximates the distribution of image gradient,hybrid data fidelity consists of l₁ and l₂ norm,which can preserve details of the image.Secondly,since the proposed model belongs to convex difference model,we adopt the DCA to address the proposed model.Furthermore,we apply the SBI and the ALM to solve the subproblem of the DCA.Finally,in order to ensure the values of the objective function monotone decreasing,the paper proves the convergence of the algorithm.