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.