A new nonlocal nonlinear diffusion of image processing

Abstract

A novel nonlocal nonlinear diffusion is analyzed which has proven useful as a denoising tool in image processing. The equation can be viewed as a new paradigm for the regularization of the well-known Perona–Malik equation. The regularization is implemented via nonlinearity intensity reduction through fractional derivatives. Well-posedness in the weak setting is established. Global existence and convergence to the average holds in the purely diffusive limit whereas an interesting dynamic behavior is engendered by the presence of nontrivial equilibria as the intensity of the nonlinearity is increased and comes close to the one of Perona–Malik.