Image Restoration using a Nonlinear Second-order Parabolic PDE-based Scheme

Abstract

A novel anisotropic diffusion-based image denoising and restoration approach is proposed in this paper. A variational model for image restoration is introduced first, then the corresponding Euler-Lagrange equation being determined. A nonlinear parabolic PDE model is then obtained from this equation. It is based on a novel edge-stopping function and conductance parameter. A serious mathematical treatment is performed on this second-order anisotropic diffusion scheme, its well-possedness being investigated. Then, a consistent explicit numerical approximation scheme based on the finite difference method is developed for the proposed PDE model.

Keywords

• image denoising and restoration
• qualitative properties of solutions
• boundary value problems for nonlinear parabolic pde
• leray-schauder principle
• edge-stopping function
• finite differences
• numerical approximation scheme.
• primary 35bxx
• 94a08
• secondary 35k55
• 35k60
• 35qxx
• 65nxx
• 68u10