Variational Image Denoising Approach with Diffusion Porous Media Flow

Abstract

A novel PDE-based image denoising approach is proposed in this paper. One designs here a nonlinear filter for image noise reduction based on the diffusion flow generated by the porous media equation $\partial u/\partial t=\mathrm{\Delta }\beta (u)$, where $\beta$ is a nonlinear continuous function of the form $\beta (u)=\lambda u^m$, . With respect to standard 2D Gaussian smoothing and some nonlinear PDE-based filters, this one is more efficient to remove noise from degraded images and also to reduce “staircasing” effects and preserve the image edges.