Hybrid Lattice Boltzmann Model for Nonlinear Diffusion and Image Denoising

Oleg Ilyin ()
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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

Mathematics, 2023, vol. 11, issue 22, 1-12

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.

Keywords: lattice Boltzmann; Perona–Malik equation; nonlinear diffusion; image denoising (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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