Useful Noise Effect for Nonlinear PDE Based Restoration of Scalar Images

Abstract

It is progressively realized that noise can play a constructive role in the domain of nonlinear information processing. This phenomenon, also known as stochastic resonance (SR) effect, has experienced large varieties of extensions with variations concerning the type of noise, the type of information carrying signal or the type of nonlinear system interacting with the signal-noise mixture. In this article, we propose an interpretation for the mechanism of noise-enhanced image restoration with nonlinear PDE (Partial Differential Equation) recently demonstrated in literature. More precisely, a link is established between the action of noise in a nonlinear Perona–Malik anisotropic diffusion and stochastic resonance in memoryless nonlinear systems for 1-D signals. For illustration some preliminary results are presented on classical “cameraman” image and the inner of SR mechanism is theoretically and practically studied using a simple set of parameters regarding the PDE used and the modeling of boundaries within images.