Multiple relaxation time lattice Boltzmann schemes for advection-diffusion equations with application to radar image processing

Michelet, Jordan; Tekitek, Mohamed Mahdi; Berthier, Michel

doi:10.1016/j.jcp.2022.111612

Cited by 11 publications

(4 citation statements)

References 22 publications

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“…The Rudin-Osher-Fatemi total variation minimization equation for image restoration [29] can be efficiently modeled using a nine-velocity LB scheme [30]. Nine-velocity MRT LB models are applied for the simulation of a nonlinear reaction-advection-diffusion equation with a constant diffusion coefficient and non-constant advection velocity, with applications in sea clutter denoising in marine radar images [31]. LB models simulating anisotropic diffusion equations can be used for the smoothing and segmentation of two-dimensional and three-dimensional medical images [32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Hybrid Lattice Boltzmann Model for Nonlinear Diffusion and Image Denoising

Ilyin

2023

Mathematics

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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.

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Section: Introductionmentioning

confidence: 99%

Hybrid Lattice Boltzmann Model for Nonlinear Diffusion and Image Denoising

Ilyin

2023

Mathematics

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“…Although they appear more complex, MRT LB schemes have significant advantages over simple SRT LB schemes, which explain their growing popularity. They allow, for instance, a gain in numerical stability [24] and a better handling of both boundary conditions [21] and physical quantities [9]. They include for instance cumulant [10] and entropic [18] LB schemes.…”

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confidence: 99%

“…Choosing equal relaxation times within the MRT collision operator leads to SRT collision operator. It is precisely because we can choose different relaxation times within the collision step that the numerical stability is improved (see for instance [24]). Following [15] and assuming all relaxation times s k nonzero for k = 1, 2, .…”

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Lattice Boltzmann convection-diffusion model with non-constant advection velocity

Michelet¹,

Tekitek²,

Berthier³

2024

DCDS-S

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The main objective of this contribution is to investigate multiple relaxation time lattice Boltzmann schemes for convection-diffusion equations.In particular, we discuss the issue of obtaining second order exact schemes when the advection velocity is non-constant. Our study is based on previous results by the authors that allow to identify the extra term, coming from the non-constancy of the advection velocity, that prevent the exactness of such schemes. We show how these terms can be cancelled, either by a suitable choice of the momentum equilibrium or by adding a forcing term applied to the non-conserved momentum. It leads to the same expression of the momentum collision. Numerical experiments are performed using Poiseuille, Couette and Taylor-Green flows. They show that the proposed momentum collision increases the numerical convergence rate up to two.

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Lattice Boltzmann model for diffusion equation with reduced truncation errors: Applications to Gaussian filtering and image processing

Ilyin

2023

Applied Mathematics and Computation

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Multiple relaxation time lattice Boltzmann schemes for advection-diffusion equations with application to radar image processing

Cited by 11 publications

References 22 publications

Hybrid Lattice Boltzmann Model for Nonlinear Diffusion and Image Denoising

Hybrid Lattice Boltzmann Model for Nonlinear Diffusion and Image Denoising

Lattice Boltzmann convection-diffusion model with non-constant advection velocity

Lattice Boltzmann model for diffusion equation with reduced truncation errors: Applications to Gaussian filtering and image processing

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