Sparse Randomized Kaczmarz for Support Recovery of Jointly Sparse Corrupted Multiple Measurement Vectors

TL;DR

This paper introduces a stochastic Sparse Randomized Kaczmarz algorithm tailored for support recovery in jointly sparse corrupted MMV problems, demonstrating robustness and effectiveness in streaming and noisy environments.

Contribution

It proposes a novel variant of the Sparse Randomized Kaczmarz algorithm specifically designed for corrupted MMV support recovery, with empirical validation.

Findings

Robustness to corruption distribution and number of corruptions

Effective support recovery in online streaming scenarios

Outperforms existing Kaczmarz-based methods

Abstract

While single measurement vector (SMV) models have been widely studied in signal processing, there is a surging interest in addressing the multiple measurement vectors (MMV) problem. In the MMV setting, more than one measurement vector is available and the multiple signals to be recovered share some commonalities such as a common support. Applications in which MMV is a naturally occurring phenomenon include online streaming, medical imaging, and video recovery. This work presents a stochastic iterative algorithm for the support recovery of jointly sparse corrupted MMV. We present a variant of the Sparse Randomized Kaczmarz algorithm for corrupted MMV and compare our proposed method with an existing Kaczmarz type algorithm for MMV problems. We also showcase the usefulness of our approach in the online (streaming) setting and provide empirical evidence that suggests the robustness of the proposed method to the distribution of the corruption and the number of corruptions occurring.