Study On Total Variation And Wavelet Frame Based Image Restoration Models And Methods

Nowadays,the research of models and algorithms for image restoration has becoming a hot issue.In recent decades,many scholars have already applied the following theories knowledge into image restoration problems: wavelet frame,total variation,sparse representation and compression perception,etc.In this paper,we propose two kinds of image restoration models and briefly describe them as follows:In this paper,we propose a model based on TVL1 for image restoration and formulate a new fixed point algorithm to solve the model for image deblurring,denoising and inpainting.The model is a problem to minimize the sum function of a data fidelity term in the L1 norm,a term in L2 norm and the total variation regularization term,the sum function is a strictly convex function.At first,by using some theory knowledge about proximity operator and subdifferential,we prove that the solution of the model can get by finding a fixed point of a nonlinear mapping.The nonlinear mapping is explicitly given in this paper.Next,we analyses the nonexpansivity of the nonlinear mapping,and this formulation leads to a new fixed point algorithms to solve the model.At last,the numerical experiments demonstrate the proposed algorithms performs favorably.In this paper,we propose a new L0 norm minimization model based on wavelet frame for image restoration and use the penalty decomposition methods to solve the model for image deblurring and denoising.The model is a problem to minimize the sum of a data fidelity term and a regularization term.The data fidelity term are three kinds of functions and the regularization term is the L0 norm of framelet coefficients of the underlying image.By using knowledge about some basic mathematical concepts and optimization theory,we analyses the convergence of the penalty decomposition methods and present the detailed process of the solution of this model.As the data fidelity term are three kinds of functions,we get three different algorithms of using the penalty decomposition methods solving the model.Numerical experiments show that the three algorithms proposed in this paper performs favorably.