Robust sparse recovery for compressive sensing in impulsive noise using ℓp-norm model fitting
Fei Wen, Peilin Liu, Yipeng Liu, Robert C. Qiu, Wenxian Yu
Abstract
This work considers the robust sparse recovery problem in compressive sensing (CS) in the presence of impulsive measurement noise. We propose a robust formulation for sparse recovery using the generalized lp-norm with 0 < p < 2 as the metric for the residual error under l1-norm regularization. An alternative direction method (ADM) has been proposed to solve this formulation efficiently. Moreover, a smoothing strategy has been used to derive a convergent method for the nonconvex case of p < 1. The convergence conditions of the proposed algorithm for both the convex and nonconvex cases have been provided. Numerical simulations demonstrated that the new algorithm can achieve state-of-the-art robust performance in highly impulsive noise.
BibTeX
@inproceedings{icassp2016_robustsparsereco,
title = {Robust sparse recovery for compressive sensing in impulsive noise using ℓp-norm model fitting},
author = {Fei Wen and Peilin Liu and Yipeng Liu and Robert C. Qiu and Wenxian Yu},
booktitle = {ICASSP 2016},
year = {2016}
}