A New Diffusion Model Besic On PDE And Classified Diffusion

Partial differential equation, as a new tool of image restoration in pasted thirty years, has injected new vitality to many image-processing-related fields. Image restoration is one of the most important parts of image processing, which is trying to turn the degraded images to clear high-quality pictures. As we know that, image information distribute in edge, noise can be anywhere, the two situations make denoising and details-protect to be a contradiction. However, traditional filters cannot deal with this problem. With the idea of edge protected and anisotropic diffusion introduce by PDEs, this contradiction can be well resolved.This thesis is only focus on denoising problem, involved the restoration models, denoising methods and idea of noise removal three aspects. The main original contributions of this thesis are summarized as follows:1. The classic model-PM model can cause reverse diffusion, which make the model instable. After analyzed the diffusion coefficient function of Perona&Malik (P-M) model, too sensitive at edge is the main reason for P-M model's ill-posed. Some amendments have done to the function, we got a posed diffusion model.2. Proposed three discrete methods for a anisotropic diffusion operator. Anosotropic diffusion is based on the direction of image features. To avoid the damage, the smoothing has to be controlled one principle: minimal smoothing in the directions across the image features, and maximal smoothing in the directions along the image features.3. Introduce a new diffusion way:classified diffusion. Smoothing is the only way that traditional diffusion to remove noise. However, marginal noise cannot be well smoothed, as a result, the smoothness of image cannot be improved a lot. Classified diffusion can be divided into two parts, noise-reduction and smoothing. The part of noise-reduction is to reduce the extent of marginal noise, that to be a minor noise. The other part is to remove minor noise, smoothing the image. Under two parts work, the image can be processed into a clear picture.