Non-local Means Denoising Algorithm Based On The Variational Method

Image denoising being an important branch of computer image processing is one of forelands. Calculus of variations and partial differential equations(PDEs) arouse tremendous research for its strong adaptability and the anisotropy diffusion characteristic. By transforming the abstract image problem into mathematical model, good models can be designed for maintaining good boundaries information, and also less calculating time. However, the method treats high frequency as noise. So it can not perform great on texture because some of the information can be smoothing as noise; Non-local Means method arouses tremendous research for its great performing on texture processing, the method utilizes the information redundancy of the image, it computes the similarity of the noise point and those in the searching windows, using the weighting average to do information compensating and denoise the image.This paper mainly does a research on combining Calculus of variations and Non-local Means method, including nonlinear and linear diffusion, which is based on having a profound understanding on both of them. a new Non-local Means algorithm based PM models is introduced and use Split Bregman to realize the numerical computation and improve the efficiency of the algorithm and denosing. The main work of the paper include the following aspects:first, introduce the concept of variations, and take TV model for example, introduce its derivation, numerical method and result of repair; second, after the introduction and analysis of Non-local mean filtering method, by combining conventional linear diffusion model and Non-local Means algorithm, design a linear Non-local diffusion model and at last introduce a special kind of Non-local Means linear rules of operator, third, based on a series of new concepts including weight and Non-local gradient, introduce a new Non-local means denoising algorithm based on anisotropic diffusion PM model and uses the Split Bregman Method for numerical computation, the simulation results demonstrate the new model perform well in time efficiency and effectiveness of the denoising effect. Finally, it is the next step for the future research.