Combined higher order non-convex total variation with overlapping group sparsity for impulse noise removal

A typical approach to eliminate impulse noise is to use the l(1)-norm for both the data fidelity term and the regularization terms. However, the l(1)-norm tends to over penalize signal entries which is one of its underpinnings. Hence, we propose a variational model that uses the non-convex l(p)-norm, 0 < p < 1 for both the data fidelity and a second-order total variation regularization term combined with an overlapping group sparse regularizer. Specifically, to robustly eliminate impulse noise, the proposed method uses a non-convex data fidelity term. The hybrid combination of a second-order non-convex total variation and an overlapping group sparse regularization term is used to eliminate the remaining staircase artifacts while maintaining a sharp restored image. A mathematical formulation is derived and to implement it, the iterative re-weighted l(1) (IRL1) based alternating direction method of multipliers (ADMM) is used to solve the constraints and the subproblems. Experimental results for image denoising and deblurring on several widely used standard images demonstrate that the proposed method performed better when compared to the l(1)-norm total variation (TV), total generalized variation (TGV) model, and the non-convex l(p)-norm TV-based data fidelity model in terms of peak signal-to-noise ratio (PSNR) and structure similarity index measure (SSIM).