Comparison Of Regularization Parameter Selection Methods In Total Variation Image Restoration

Image restoration is a very important aspect of digital image processing. Image restoration is an ill-posed inverse problem. It can be solved by regularization method. The main content of this thesis is listed as follows:Firstly, the mathematical theory of regularization method and the ill posedness of inverse problem are introduced. That the Image restoration is a typical ill-posed problem is mentioned. The process of image degradation is analyzed. The discrete model of image restoration is constructed.Secondly, Two typical regularization method are introduced, i.e. the method of Tikhonov(TK) and Total Variation (TV), and several adaptive selection methods of regularization parameter are describe. The advantages and disadvantages of different regularization parameter selection methods are compared and analyzed. The GCV regularization parameter selection method is discussed in detail. Meanwhile, two fast implementation methods of image restoration are introduced.Finally, since the parameter adaptive selection of TV regularization method is more difficult to be dealt with because of its non-linear regularization part, the approximate linear regularization method is adopted. An improved GCV method is adopted for the algorithm of selecting regularization parameter. Based on this, a new improved GCV regularization parameter selection method is put forward. In the end, numerical simulation results indicate that the improved method is feasible and optimal.