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A novel PDE based image restoration: Convection-diffusion equation for image denoising. (English) Zbl 1169.94006
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 [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.

94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
68U10 Computing methodologies for image processing
76M10 Finite element methods applied to problems in fluid mechanics
Full Text: DOI
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