An improved anisotropic diffusion PDE for noise removal and edge preservation

In this paper, an improved anisotropic nonlinear diffusion equation for image restoration is presented. As a corner in an image is rounded when using degenerated diffusion equation. to smooth the image, it proposed to use both the gradient and the second order directional derivative in the direction orthogonal to the gradient to control the diffusion velocity. It can remove noise and perform stably. It can also enhance step-like edges and keep the locality of them. Compared with other method, it is capable of keeping stronger peaks and thin edges. Due to these characteristics, not only the processed noisy image look much more clear and smooth, but also the details are kept, resulting in the naturalness. The experiment results are very satisfactory.