<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>We analyze a finite volume scheme for a nonlinear reaction-diffusion system applied to image processing. First, we demonstrate the existence of a solution to the finite volume scheme. Then, based on the derivation of a series of a priori estimates and the use of Kolmogorov’s compactness criterion, we prove that the solution to the finite volume scheme converges to the weak solution. In the numerical experiments, we show the effectiveness of the proposed model with respect to the modified (in the sense of Catté, Lions, Morel and Coll) Perona-Malik nonlinear image selective smoothing equation in terms of preserving small details, texture, and fine structures.</p>
</abstract>

We analyze a finite volume scheme for a nonlinear reaction-diffusion system applied to image processing. First, we demonstrate the existence of a solution to the finite volume scheme. Then, based on the derivation of a series of a priori estimates and the use of Kolmogorov’s compactness criterion, we prove that the solution to the finite volume scheme converges to the weak solution. In the numerical experiments, we show the effectiveness of the proposed model with respect to the modified (in the sense of Catté, Lions, Morel and Coll) Perona-Malik nonlinear image selective smoothing equation in terms of preserving small details, texture, and fine structures.

Convergence of a finite volume scheme for a parabolic system applied to image processing

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

We analyze a finite volume scheme for a nonlinear reaction-diffusion system applied to image processing. First, we demonstrate the existence of a solution to...

Convergence of a finite volume scheme for a parabolic system applied to image processing

Published Online: Oct 11, 2022

Page range: 401 - 437

Received: Jun 18, 2022

Accepted: Sep 24, 2022

DOI: https://doi.org/10.2478/mjpaa-2022-0027

Keywords
Image Processing, Perona-Malik Equation, Finite Volume Method, Convergence, nonlinear reaction-diffusion

© 2022 Jamal Attmani et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Convergence of a finite volume scheme for a parabolic system applied to image processing

Published Online: Oct 11, 2022

Page range: 401 - 437

Received: Jun 18, 2022

Accepted: Sep 24, 2022

DOI: https://doi.org/10.2478/mjpaa-2022-0027

KeywordsImage Processing, Perona-Malik Equation, Finite Volume Method, Convergence, nonlinear reaction-diffusion

© 2022 Jamal Attmani et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Image Processing, Perona-Malik Equation, Finite Volume Method, Convergence, nonlinear reaction-diffusion