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

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