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Keywords = Perona–Malik equation

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12 pages, 1089 KiB  
Article
Hybrid Lattice Boltzmann Model for Nonlinear Diffusion and Image Denoising
by Oleg Ilyin
Mathematics 2023, 11(22), 4601; https://doi.org/10.3390/math11224601 - 10 Nov 2023
Cited by 3 | Viewed by 1325
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Mathematical Modeling, Optimization and Machine Learning, 2nd Edition)
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