A New Bound on Approximate Support Recovery

TL;DR

This paper provides a new theoretical bound on the support recovery performance of orthogonal matching pursuit (OMP) in noisy conditions, showing it can achieve arbitrarily small error rates under mild conditions.

Contribution

It establishes a novel bound demonstrating that OMP's support recovery error rate is independent of the maximum element of the signal, confirming a conjecture from prior work.

Findings

OMP can recover support with arbitrarily small error under certain conditions.

Support recovery error rate is independent of the maximum signal element.

The analysis confirms a conjecture from Wang (2015).

Abstract

Orthogonal matching pursuit (OMP) is a greedy algorithm popularly being used for the recovery of sparse signals. In this paper, we study the performance of OMP for support recovery of sparse signal under noise. Our analysis shows that under mild constraint on the minimum-to-average ratio of nonzero entries in the sparse signal and the signal-to-noise ratio, the OMP algorithm can recover the support of signal with an error rate that can be arbitrarily small. Our result offers an affirmative answer to the conjecture of [Wang, TSP 2015] that the error rate of support recovery via OMP has no dependence on the maximum element of the signal.