A new feature-preserving nonlinear anisotropic diffusion method for image denoising

We present a new diffusion method for noise reduction and feature preservation.Presently, denoising methods commonly use a first-order derivative to detect edges inorder to achieve a good balance between noise removal and feature preserving.However, if edges are partly lost to a certain extent or contaminated severely bynoise, these methods may not be able to detect them and thus fail to preserve variousfeatures in images. To overcome this problem, we propose a new and moresophisticated feature detector by combining first- and second-order derivatives for anonlinear anisotropic diffusion model. Numerical experiments show that the newdiffusion filter outperforms many popular filters for denoising images containingedges, blobs and ridges and textures made of these features

A new nonlocal nonlinear diffusion equation for image denoising and data analysis

In this paper we introduce and study a new feature-preserving nonlinear anisotropic diffusion for denoising signals. The proposed partial differential equation is based on a novel diffusivity coefficient that uses a nonlocal automatically detected parameter related to the local bounded variation and the local oscillating pattern of the noisy input signal. We provide a mathematical analysis of the existence of the solution of our nonlinear and nonlocal diffusion equation in the two dimensional case (images processing). Finally, we propose a numerical scheme with some numerical experiments which demonstrate the effectiveness of the new method