Analysis of orthogonal matching pursuit using the restricted isometry property

Authors:
Mark A. Davenport;Michael B. Wakin
Affiliations:
Department of Statistics, Stanford University, Stanford, CA;Division of Engineering, Colorado School of Mines, Golden, CO
Venue:
IEEE Transactions on Information Theory
Year:
2010

Citing 8
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Abstract

Orthogonal matching pursuit (OMP) is the canonical greedy algorithm for sparse approximation. In this paper we demonstrate that the restricted isometry property (RIP) can be used for a very straightforward analysis of OMP. Our main conclusion is that the RIP of order K + 1 (with isometry constant δ K) is sufficient for OMP to exactly recover any K-sparse signal. The analysis relies on simple and intuitive observations about OMP and matrices which satisfy the RIP. For restricted classes of K-sparse signals (those that are highly compressible), a relaxed bound on the isometry constant is also established. A deeper understanding of OMP may benefit the analysis of greedy algorithms in general. To demonstrate this, we also briefly revisit the analysis of the regularized OMP (ROMP) algorithm.