Year: 2021
Author: Anis Theljani
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 1 : pp. 38–61
Abstract
We consider a class of nonstandard high-order PDEs models, based on the ($p(·)$, $q(·)$)-Kirchhoff operator with variable exponents for the image denoising problem. We theoretically analyse the proposed non-linear model. Then, we use linearization method based on a fixed-point iterative technique and we also prove the convergence of the iterative process. The model has a multiscale character which follows from an adaptive selection of the exponents $p(·)$ and $q(·)$. The latter task helps to capture, highlight and correlate major features in the images and optimize the smoothing effect. We use Morley finite-elements for the numerical resolution of the proposed model and we give several numerical examples and comparisons with different methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2021-IJNAM-18620
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 1 : pp. 38–61
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24