| Issue |
ESAIM: M2AN
Volume 59, Number 3, May-June 2025
|
|
|---|---|---|
| Page(s) | 1705 - 1727 | |
| DOI | https://doi.org/10.1051/m2an/2025043 | |
| Published online | 30 June 2025 | |
Gaussian and Poisson noise identification using non-convex optimization with L2-norm power constraints
1
EMI, Sultan Moulay Slimane University, Beni-Mellal, Morocco
2
ENSA Khouribga, EMI, Université Sultan Moulay Slimane, Beni-Mellal, Morocco
3
LAB SIV, Ibno Zohr University, Agadir, Morocco
* Corresponding author: laghrib.amine@gmail.com
Received:
28
May
2024
Accepted:
26
May
2025
This article tackles the main issues related to image restoration, including the preservation of contours, removal of the staircasing effect, and reduction of mixture noise. For this purpose, we introduced a novel minimization problem, based on a PDE-constrained whose nonlinear structure relies on the solution itself. For the non-convex cost function, it contains a novel regularization that strikes a balance between edge enhancement and smoothness. The model employs a robust fidelity term based on the L2-norm to ensure accurate reconstruction. A comprehensive theoretical analysis establishes the well-posedness of the model, and the ADMM method is used to solve the minimization problem. Extensive experiments demonstrate the model’s numerical efficiency and its effectiveness in addressing mixed noise and maintaining image detail.
Mathematics Subject Classification: 58F15 / 58F17
Key words: Image restoration / variable nonlinearity / non-convex function / mixture noise / nonlocal evolution equations
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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