An ℓ₀-overlapping group sparse total variation for impulse noise image restoration

Total variation (TV) based methods are effective models in image restoration. For eliminating impulse noise, an effective way is to use the ℓ₁-norm total variation model. However, the TV image restoration always yields staircase artifacts, especially in high-density noise levels. Additionally, the ℓ₁-norm tends to over penalize solutions and is not robust to outlier characteristics of impulse noise. In this paper, we propose a new total variation model to effectively remove the staircase effects and eliminate impulse noise. The proposed model uses the ℓ₀-norm data fidelity to effectively remove the impulse noise while the overlapping group sparse total variation (OGSTV) acts as a regularizer to eliminate the staircase artifacts. Since the proposed method requires solving an ℓ₀-norm and an OGSTV optimization problem, a formulation using the mathematical program with equilibrium constraints (MPEC) and the majorization–minimization (MM) method are respectively used together with the alternating direction method of multipliers (ADMM). Experiments demonstrate that our proposed model performs better than several state-of-the-art algorithms such as the ℓ₁ total generalized variation, ℓ₀ total variation, and the ℓ₁ overlapping group sparse total variation in terms of the peak signal-to-noise ratio (PSNR) and the structural similarity index measure (SSIM).