Nonconvex high-order TV and $\ell_{0}$ norm-based method for image restoration

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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 ℓ₀ norm data fidelity. This combination aided in overcoming the staircase artifacts and maintaining sharp contours while tackling the poor performance of ℓ₁ 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 ℓ₁ algorithm. Finally, numerous experiments demonstrated that the suggested scheme achieves competitive performance in terms of objective metrics and visual quality.

Keywords

image restoration / impulse noise / nonconvex function / ℓ ₀ norm / alternating direction method of multipliers

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