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Hybrid Lattice Boltzmann Model for Nonlinear Diffusion and Image Denoising

Author

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  • Oleg Ilyin

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Vavilova-44, 2, 119333 Moscow, Russia)

Abstract

In the present paper, a novel approach for image denoising based on the numerical solution to the nonlinear diffusion equation is proposed. The Perona–Malik-type equation is solved by employing a hybrid lattice Boltzmann model with five discrete velocities. In this method, the regions with large values of the diffusion coefficient are modeled with the lattice Boltzmann scheme for which hyper-viscous defects are reduced, while other regions are modeled with the conventional lattice Boltzmann model. The new method allows us to solve Perona–Malik-type equations with relatively large time steps and good accuracy. In numerical experiments, the removal of salt and pepper, speckle and Gaussian noise is considered. For salt and pepper noise, the novel scheme yields better peak signal-to-noise ratios in image denoising problems compared to the standard lattice Boltzmann approach. For certain non-small values of time steps, the novel model shows better results for speckle and Gaussian noise on average.

Suggested Citation

  • Oleg Ilyin, 2023. "Hybrid Lattice Boltzmann Model for Nonlinear Diffusion and Image Denoising," Mathematics, MDPI, vol. 11(22), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4601-:d:1277565
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    References listed on IDEAS

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    1. Shinsuke Suga, 2006. "Numerical Schemes Obtained From Lattice Boltzmann Equations For Advection Diffusion Equations," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 17(11), pages 1563-1577.
    2. Shinsuke Suga, 2009. "Stability And Accuracy Of Lattice Boltzmann Schemes For Anisotropic Advection-Diffusion Equations," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 20(04), pages 633-650.
    3. Ilyin, Oleg, 2023. "Lattice Boltzmann model for diffusion equation with reduced truncation errors: Applications to Gaussian filtering and image processing," Applied Mathematics and Computation, Elsevier, vol. 456(C).
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    1. Ilyin, Oleg, 2023. "Lattice Boltzmann model for diffusion equation with reduced truncation errors: Applications to Gaussian filtering and image processing," Applied Mathematics and Computation, Elsevier, vol. 456(C).

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