A new nonlocal nonlinear diffusion equation for image denoising and data analysis
Analysis of PDEs
2019-07-23 v1 Numerical Analysis
Abstract
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.
Cite
@article{arxiv.1707.06396,
title = {A new nonlocal nonlinear diffusion equation for image denoising and data analysis},
author = {Giacomo Aletti and Monica Moroni and Giovanni Naldi},
journal= {arXiv preprint arXiv:1707.06396},
year = {2019}
}