A Non-convex Diffusion Model for Simultaneous Image Denoising and Edge Enhancement

Mathematical restoration models, in particular, total variationbased models can easily lose fine structures during image denoising. In order to overcome the drawback, this article introduces two strategies: the nonconvex (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.