@article{Wang2025, 
author = {Ben Wang and Zijie Lan},
title = {Nonconvex high-order TV and        ℓ    0   norm-based method for image restoration},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {6},
pages = {3431-3449},
keywords = {image restoration, impulse noise, nonconvex function, ℓ0 norm, alternating direction method of multipliers},
url = {https://www.sciopen.com/article/10.3934/era.2025152},
doi = {10.3934/era.2025152},
abstract = {In order to obtain high-quality restoration outcomes, this paper proposed a new nonconvex variational model tailored for reconstructing blurred images corrupted by impulse noise. The newly designed optimization framework integrated nonconvex high-order total variation regularization with        ℓ    0   norm data fidelity. This combination aided in overcoming the staircase artifacts and maintaining sharp contours while tackling the poor performance of        ℓ    1   norm-based data fidelity in handling high-density impulse noise. To deal with the nonconvex optimization problem, we designed an efficient alternating direction method of multipliers by combining the variable splitting technique with the iteratively reweighted        ℓ    1   algorithm. Finally, numerous experiments demonstrated that the suggested scheme achieves competitive performance in terms of objective metrics and visual quality.}
}