Elimination of Impulsive Disturbance based on Nonconvex Regularization

This work aims to recovery the signal that is corrupted by impulsive disturbance. To that end, the $\ell_{p}$-norm $(0 \lt p \leq 1)$ is employed to promote sparsity of the signal of interest and the impulsive disturbance. By doing so, the signal recovery and disturbance suppression are simultaneously achieved. Two improved solvers based on block coordinate descent (BCD) and alternative direction method of multipliers (ADMM) frameworks are developed by utilizing the principle of the reweighted recursive least squares. Numerical experiments demonstrate that the superior performance of the proposed algorithms is obtained compared with the state-of-the-art proximal BCD and ADMM algorithms.