Research On Exponential Adaptive TV~p Image Restoration

In recent decades,with the continuous advancement of technology,image restoration technology has been widely used in various fields of industrial and agricultural production.Its development mainly experienced three stages:direct recovery method,regularization method and adaptive method.Because the direct restoration problem is morbid and can-not achieve the best results,this method cannot meet the needs of production and life,and is rarely used now.The regularization and adaptive method that were subsequent-ly proposed became more and more popular.First-order total variation regularization method has a significant restoration effect on the degraded image caused by the influence of noise.Although it has the disadvantage of easily generating a staircase effect,the gen-eralized total variation model(TGV)and the high-order total variation model(HDTV)based on this method can be effective overcome this shortcoming.How to combine the local information of the image with the proposed model during the restoration process and maintain the structural integrity is very important.Regarding the issue above,this thesis proposes a local adaptive TVp-regularization model based on the total variation model.The main research contents of the thesis are as follows:(1)In the model,in order to effectively characterize the image structure,the selection of the exponential parameter p ?(0,2)depends on the eigenvalue of the structure tensor and the adaptively selected threshold function.When solving the tensor matrix,the elements depend on the outer product of the gradient operator.To reduce the noise interference to the matrix,the Wiener filter is used to smooth the image.(2)When p ?(0,1),the proposed new model is a non-convex non-smooth optimiza-tion problem;when p ?(1,2),it is a convex smooth problem.Therefore,the method of variable separation and Half-quadratic method are used to transform it into a saddle point problem that can be solved alternately,and solved by the alternating direction mul-tiplier method.In addition,the convergence of the algorithm is analyzed in the thesis.Numerical experiments verify the validity and robustness of the model.