Multichannel sparse recovery of complex-valued signals using Huber's criterion

TL;DR

This paper extends Huber's criterion to multichannel complex-valued sparse recovery, introducing a robust algorithm that performs well under heavy-tailed noise and is demonstrated in source localization tasks.

Contribution

The paper develops a robust multichannel sparse recovery method using a generalized Huber's criterion and a novel SNIHT-based algorithm called HUB-SNIHT.

Findings

HUB-SNIHT is robust under heavy-tailed noise.

The method performs comparably to SNIHT under Gaussian noise.

Application demonstrated in source localization with sensor arrays.

Abstract

In this paper, we generalize Huber's criterion to multichannel sparse recovery problem of complex-valued measurements where the objective is to find good recovery of jointly sparse unknown signal vectors from the given multiple measurement vectors which are different linear combinations of the same known elementary vectors. This requires careful characterization of robust complex-valued loss functions as well as Huber's criterion function for the multivariate sparse regression problem. We devise a greedy algorithm based on simultaneous normalized iterative hard thresholding (SNIHT) algorithm. Unlike the conventional SNIHT method, our algorithm, referred to as HUB-SNIHT, is robust under heavy-tailed non-Gaussian noise conditions, yet has a negligible performance loss compared to SNIHT under Gaussian noise. Usefulness of the method is illustrated in source localization application with sensor arrays.