Diffusion filtering in image processing based on wavelet transform

Nonlinear diffusion filtering is a method for images or signals processing based on partial differential equations (PDEs). Its basic idea is to establish a suitable PDE model in the time-space domain and obtain a family of its solutions as the filtered ve…

Diffusion filtering in image processing based on wavelet transform

The nonlinear diffusion filtering in image processing bases on the heat diffu- sion equations. Its key is the control of diffusion amount. In the previous models, the dif- fusivity depends on the gradients of images. So it is easily affected by noises. This paper first gives a new multiscale computational technique for diffusivity. Then we proposed a class of nonlinear wavelet diffusion (NWD) models that are used to restore images. The NWD model has strong ability to resist noise.But it, like the previous models, requires higher computational effort. Thus, by simplifying the NWD, we establish linear wavelet diffusion (LWD) models that consist of advection and diffusion. Since there exists the ad- vection, the LWD filter is anisotropic, and hence can well preserve edges although the diffusion at edges is isotropic. The advantage is that the LWD model is easy to be ana- lyzed and has lesser computational load. Finally, a variety of numerical experiments com- pared with the previous model are shown.