Analysis of Orthogonal Matching Pursuit for Compressed Sensing in Practical Settings

TL;DR

This paper extends the theoretical understanding of Orthogonal Matching Pursuit (OMP) in compressed sensing by providing recovery guarantees for matrices with unequal column norms, reflecting more realistic practical scenarios.

Contribution

It derives new sparse recovery guarantees for OMP when the measurement matrix has unequal column norms, a common practical constraint.

Findings

Guarantees for matrices with comparable column norms

Successful support recovery under new conditions

Low mean squared error in signal estimation

Abstract

Orthogonal matching pursuit (OMP) is a widely used greedy algorithm for sparse signal recovery in compressed sensing (CS). Prior work on OMP, however, has only provided reconstruction guarantees under the assumption that the columns of the CS matrix have equal norms, which is unrealistic in many practical CS applications due to hardware constraints. In this paper, we derive sparse recovery guarantees with OMP, when the CS matrix has unequal column norms. Finally, we show that CS matrices whose column norms are comparable achieve tight guarantees for the successful recovery of the support of a sparse signal and a low mean squared error in the estimate.