A New Performance Guarantee for Orthogonal Matching Pursuit Using Mutual Coherence

TL;DR

This paper introduces a new coherence-based performance guarantee for Orthogonal Matching Pursuit, accounting for signal parameters and noise, with numerical results showing improved bounds over previous methods.

Contribution

It provides a novel probabilistic guarantee for OMP that incorporates dynamic range, noise variance, and sparsity, improving upon prior bounds.

Findings

New probabilistic support recovery bound for OMP

Inclusion of signal parameters in the guarantee

Numerical simulations demonstrate improved performance bounds

Abstract

In this paper we present a new coherence-based performance guarantee for the Orthogonal Matching Pursuit (OMP) algorithm. An upper bound for the probability of correctly identifying the support of a sparse signal with additive white Gaussian noise is derived. Compared to previous work, the new bound takes into account the signal parameters such as dynamic range, noise variance, and sparsity. Numerical simulations show significant improvements over previous work.