Improving the Correlation Lower Bound for Simultaneous Orthogonal Matching Pursuit

TL;DR

This paper introduces a new lower bound on the correlation metric used in SOMP, improving theoretical understanding and performance analysis, especially in noisy scenarios, for joint sparse signal recovery.

Contribution

It provides a novel lower bound for the correlation metric in SOMP, enhancing analysis accuracy and outperforming existing bounds for specific signal patterns.

Findings

The new bound improves the analysis of SOMP in noiseless cases.

It outperforms state-of-the-art bounds for certain signal patterns.

The bound is useful for noisy signal recovery analysis.

Abstract

The simultaneous orthogonal matching pursuit (SOMP) algorithm aims to find the joint support of a set of sparse signals acquired under a multiple measurement vector model. Critically, the analysis of SOMP depends on the maximal inner product of any atom of a suitable dictionary and the current signal residual, which is formed by the subtraction of previously selected atoms. This inner product, or correlation, is a key metric to determine the best atom to pick at each iteration. This paper provides, for each iteration of SOMP, a novel lower bound of the aforementioned metric for the atoms belonging to the correct and common joint support of the multiple signals. Although the bound is obtained for the noiseless case, its main purpose is to intervene in noisy analyses of SOMP. Finally, it is shown for specific signal patterns that the proposed bound outperforms state-of-the-art results for SOMP, and orthogonal matching pursuit (OMP) as a special case.