A new hybrid regularization scheme for removing salt and pepper noise

We propose a new model for removing the Salt and Pepper Noise (SPN) by combining the high-order total variation overlapping group sparsity with the nuclear norm regularization. Since the proposed model is convex, non-smooth, and separable, the alternating direction method of multipliers (ADMM) can be employed to solve it and the convergence can be kept. Numerical comparisons with some related state-of-the-art models show that the proposed model can significantly improve the restored quality in terms of the signal to noise ratio (SNR) and the structural similarity index measure (SSIM).