Rigorous mathematical investigation of a nonlinear anisotropic diffusion-based image restoration model

Abstract

A nonlinear diffusion based image denoising technique is introduced in this paper. The proposed PDE denoising and restoration scheme is based on a novel diffusivity function that uses an automatically detected conductance parameter. A robust mathematical treatment is also provided for our anisotropic diffusion model. We demonstrate that edge-stopping function model is properly chosen, explaining the mathematical reasons behind it. Also, we perform a rigorous mathematical investigation on of the existence and uniqueness of the solution of our nonlinear diffusion equation. This PDE-based noise removal approach outperforms most diffusion-based methods, producing considerably better smoothing results and providing a much better edge preservation.

Keywords

• Edge-preserving image denoising
• nonlinear anisotropic diffusion
• PDE model
• edge-stopping function
• diffusivity conductance parameter