Nonlinear Diffusion Combined with Brownian Motions for Image Denoising

We introduce Brownian motion into the nonlinear diffusion process for image denoising in this paper. Brownian motion in our work stands for the variation of gray value of a pixel in the form of "random walking" which analogs the irregular and unceasing movement of a small particle. A reflection wall is set for each pixel to force its Brownian motion to act as an inverse process of the diffusion process. Moreover, the absorption walls are also set to limit the range of the distance of Brownian motion in order to overcome the inherent unstability of the inverse process. The parameters of Brownian motion and the location of the reflection and absorption walls are estimated adaptively according to the local feature of the neighborhood of the corresponding pixel. The method of the combination of the nonlinear diffusion and Brownian motion is called as ND-BM method. The experimental results shows that it is one of effective method for image denoising.