On The Exact Recovery Condition of Simultaneous Orthogonal Matching Pursuit

TL;DR

This paper extends recent exact recovery criteria for orthogonal matching pursuit (OMP) to the simultaneous OMP (SOMP) algorithm, which handles multiple measurement vectors, and discusses the bounds' sharpness.

Contribution

It demonstrates that existing ERC for OMP are valid for SOMP, a generalized version capable of processing multiple signals simultaneously.

Findings

ERC for OMP are valid for SOMP.

Bounds' sharpness is discussed in context of previous OMP results.

SOMP can recover common support of multiple sparse signals.

Abstract

Several exact recovery criteria (ERC) ensuring that orthogonal matching pursuit (OMP) identifies the correct support of sparse signals have been developed in the last few years. These ERC rely on the restricted isometry property (RIP), the associated restricted isometry constant (RIC) and sometimes the restricted orthogonality constant (ROC). In this paper, three of the most recent ERC for OMP are examined. The contribution is to show that these ERC remain valid for a generalization of OMP, entitled simultaneous orthogonal matching pursuit (SOMP), that is capable to process several measurement vectors simultaneously and return a common support estimate for the underlying sparse vectors. The sharpness of the bounds is also briefly discussed in light of previous works focusing on OMP.