A image denoising by modified nonlocal means method based on generalized cross-validation

Nonlocal means method (NLM) is a powerful algorithm in image denoising area. In this article, firstly its modified expression is defined, and then generalized cross validation (GCV) method is used to approximate the optimal value of two parameters in this expression. At the same time, the analytical formula of GCV method can also be derived from modified expression. As a result, the restoration image processed by optimal value of parameters is mostly close to the original noise-free image and their mean square error (MSE) is nearly minimal compared with others. Finally, the experimental results show the performance of noise reduction by different methods.