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 - <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>