A Bilevel Optimization Approach For Learning Spatially-Dependent TV-L₁ Parameter In Image Denoising

In this work,we consider the problem of spatially dependent parameter learning in TV-L1 image denoising model.We obtain the weight function by the bilevel optimization method to denoising the non-uniform noises in image processing.A brief summary of our work is as follows.The introduction in the first chapter tells the significance of the variational model in dealing with image denoising and how to use the bilevel optimization method to learn the weight function.Then it introduces the research progresses of various people in this field in recent years.In chapter 2 we give the TV-L1 denoising model and its bilevel optimization problem on functional space.After proving the existence of the optimal solution,the regularization version of the bilevel problem is given and the first and second order differentiability of its solution operator is proved.Then,by the differentiability properties of the solution operator,the first-order optimization condition and the second-order necessary condition of the optimal solution of the bilevel optimization problem are derived,and the first-order optimization condition is complimented into the equation form.In chapter 3 we give the discretization schme of the problem and discretize the optimal conditions.Since the system is semi-smooth,we use the semi-smooth Newton method to find the optimal solution in discretization schme and prove the local superlinear convergence of the given algorithm.Of course,in order to show the results of the algorithm,we carry out numerical simulation in chapter 4.It is obvious that our algorithm's denoising effect is remarkable,especially for non-uniform noises.