Impulse noise removal by using a nonconvex TGV regularizer and nonconvex fidelity

With the aim of acquiring high-quality restored images, this paper derives a novel nonconvex variational model for the removal of impulse noise. The investigated solver integrates the superiorities of nonconvex second-order total generalized variation (TGV) regularization and nonconvex data fidelity. More precisely, the usage of a nonconvex TGV regularizer helps to eliminate the staircase artifacts and simultaneously preserve edge details. Nonconvex fidelity, which enhances sparsity, is adopted to effectively detect impulse noise. Computationally, incorporating the popular iteratively reweighted ℓ1 algorithm and variable splitting method, we propose to adopt an efficient alternating direction method of multipliers for the purpose of rapidly resolving the designed optimization problem. Additionally, simulation examples have been executed to compare our method with several state-of-the-art techniques. Experimental results and quantitative comparisons confirm that the developed strategy outperforms other competitors for suppressing impulse noise (even high density) in both visual outcomes and recovery accuracy.