A novel PDE based image restoration: Convection-diffusion equation for image denoising

Authors:
Y. Shih;C. Rei;H. Wang
Affiliations:
Department of Applied Mathematics, National Chung Hsing University, 250 Kuo-Kuang Road, Taichung 40227, Taiwan;Department of Applied Mathematics, National Chung Hsing University, 250 Kuo-Kuang Road, Taichung 40227, Taiwan;Department of Applied Mathematics, National Chung Hsing University, 250 Kuo-Kuang Road, Taichung 40227, Taiwan
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

In this paper we present a convection-diffusion equation for processing image denoising, edge preservation and compression. We compare it with a popular nonlinear diffusion model which has been widely implemented in image denoising for Gaussian white noise. Here we show that this convection-diffusion model effectively removes noise, especially for the mixture of Gaussian and salt-and-pepper noises. We propose the modified streamline diffusion method [Y. Shih, H.C. Elman, Modified streamline diffusion schemes for convection-diffusion problems, Comput. Methods Appl. Mech. Eng, 1998.] for the discretization of this convection-diffusion model to prevent internal layers because of the discontinuities while using the coarsening algorithm for the image compression. Numerical experiments have shown that our convection-diffusion model for removing both Gaussian and salt-and-pepper noises, efficiently and reliably preserves edges quite satisfactorily.