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Zbl 1169.94006
Shih, Y.; Rei, C.; Wang, H.
A novel PDE based image restoration: Convection-diffusion equation for image denoising. (English)
[J] J. Comput. Appl. Math. 231, No. 2, 771-779 (2009). ISSN 0377-0427

Summary: 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 [{\it Y. Shih, H. C. Elman}, Comput. Methods Appl. Mech. Eng. 174, No. 1--2, 137--151 (1999; Zbl 0957.76035)] 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.

MSC 2000:: *94A08 Image processing
65M50 Mesh generation and refinement (IVP of PDE)
65M60 Finite numerical methods (IVP of PDE)
68U10 Image processing
76M10 Finite element methods

Keywords: image denoising; edge detection; compression; streamline diffusion method; adaptive finite element; convection-diffusion

Citations: Zbl 0957.76035

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