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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.

MSC:
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
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