@Article{IJNAM-18-1,
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 = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/2021-IJNAM-18620},
url = {https://global-sci.com/article/82968/multi-scale-non-standard-fourth-order-pde-in-image-denoising-and-its-fixed-point-algorithm}
}