@article{Hakoume2022, 
author = {Abdelmajid El Hakoume and Lekbir Afraites and Amine Laghrib},
title = {An improved coupled PDE system applied to the inverse image denoising problem},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {7},
pages = {2618-2642},
keywords = {image denoising, fixed point theorem, high order PDE system, anisotropic diffusion tensor},
url = {https://www.sciopen.com/article/10.3934/era.2022134},
doi = {10.3934/era.2022134},
abstract = {The problem of interest in this paper is the mathematical and numerical analysis of a new non-variational model based on a high order non-linear PDE system resulting from image denoising. This model is motivated by involving the decomposition approach of  H−1 norm suggested by Guo et al. [1,2] which is more appropriate to represent the small details in the textured image. Our model is based on a diffusion tensor that improves the behavior of the Perona-Malik diffusion directions in homogeneous regions and the Weickert model near tiny edges with a high diffusion order. A rigorous analysis of the existence and uniqueness of the weak solution of the proposed reaction-diffusion model is cheked in a suitable functional framework, using the Schauder fixed point theorem. Finally, we carry out a numerical result to show the effectiveness of our model by comparing the results obtained with some competitive models.}
}