Nonconvex high-order TV and ${\ell }_0$ norm-based method for image restoration

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 ${\ell }_0$ norm data fidelity. This combination aided in overcoming the staircase artifacts and maintaining sharp contours while tackling the poor performance of ${\ell }_1$ 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 ${\ell }_1$ algorithm. Finally, numerous experiments demonstrated that the suggested scheme achieves competitive performance in terms of objective metrics and visual quality.