Nonconvex Non-lipschitzian Image Restoration Using Regularization Parameter Selection Based On Generalized Cross Validation

The study of ill posed problems plays a very important role in the theory?algorithm and application of mathematical optimization.Many ap-plications are concerned with the problem of parameter estimation,e.g.,image restoration.There are a variety of methods to estimate the regularization param-eters,such as the commonly used L-curve method,the cross validation method and the generalized cross validation method.etc..In this paper,we mainly study nonconvex non-Lipschitzian image restoration using the regularization parameter selection based on generalized cross validation.We use nonconvex non-Lipschitzian Lp(0<p<1)regularization term which helps to recover distinct edges.The alter-nating minimization framework,the smoothing steepest descent algorithm,as well as golden section line search for one dimension optimization are adopted,to adjust the regularization parameter as well as image restoration.From the restoration results of images and different,levels of noise,we find that our nonconvex non-Lipschitzian model provides the highest signal-to-noise ratio(SNR),compared to the models of LTV and L1 regularization terms.using the generalized cross valida-tion method for regularization parameter selection.