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.

I. Introduction

The signal recovery is an important application where the objective is to reconstruct the clean signal from the disturbance corrupted measurements. Speaking of disturbance, Gaussian noise is used very often because Gaussian distribution presents a closed-form expression of probability density function (PDF) and therefore, it is easy to handle. In addition to that, if certain structure of signal is exploited, different approaches are developed over the years to exploit the structures. For example, if the sparse property of signal of interest is utilized, the compressed sensing (CS) theory states that the signal can be recovered from a small percentage of measurements by solving optimization problem of minimize , where is -norm to promote signal sparsity. This approach and its improved versions are successfully applied across different fields such as image processing [1], [2], speech processing [3] – [5], MRI [6], [7], interference suppression in radar signals [8] and many more.