Sixth Mississippi State Conference on Differential Equations and
Computational Simulations.
Electronic Journal of Differential Equations,
Conference 15 (2007), pp. 175-192. 

Title: A non-convex diffusion model for simultaneous 
       image denoising and edge enhancement

Authors: Seongjai Kim (Mississippi State Univ., MS, USA)
         Hyeona Lim  (Mississippi State Univ., MS, USA)
 
Abstract: 
 Mathematical restoration models, in particular, total variation-based
 models can easily lose fine structures during image denoising.
 In order to overcome the drawback, this article introduces two
 strategies: the non-convex (NC) diffusion and the texture-free residual
 (TFR) parameterization.
 A non-standard numerical procedure is suggested and its stability
 is analyzed to effectively solve the NC diffusion model which is
 mathematically unstable.
 It has been numerically verified that the resulting algorithm
 incorporating the NC diffusion and TFR parameterization is able to not
 only reduce the noise satisfactorily but also enhance edges effectively,
 at the same time.
 Various numerical examples are shown to confirm the claim.

Published February 28, 2007.
Math Subject Classifications: 35K55, 65M06, 65M12.
Key Words: Fine structures; denoising; edge enhancement; 
           nonphysical dissipation; total variation (TV) model;
           non-convex (NC) diffusion model; 
           texture-free residual (TFR) parameterization.