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Volume 18, Issue 1
Multi-Scale Non-Standard Fourth-Order PDE in Image Denoising and Its Fixed Point Algorithm

Anis Theljani

Int. J. Numer. Anal. Mod., 18 (2021), pp. 38-61.

Published online: 2021-02

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  • 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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@Article{IJNAM-18-38, author = {Theljani , Anis}, title = {Multi-Scale Non-Standard Fourth-Order PDE in Image Denoising and Its Fixed Point Algorithm}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2021}, volume = {18}, number = {1}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/18620.html} }
TY - JOUR T1 - Multi-Scale Non-Standard Fourth-Order PDE in Image Denoising and Its Fixed Point Algorithm AU - Theljani , Anis JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 38 EP - 61 PY - 2021 DA - 2021/02 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/18620.html KW - AB -

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.

Anis Theljani. (2021). Multi-Scale Non-Standard Fourth-Order PDE in Image Denoising and Its Fixed Point Algorithm. International Journal of Numerical Analysis and Modeling. 18 (1). 38-61. doi:
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