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arXiv · 0909.0083

Analysis of Orthogonal Matching Pursuit using the Restricted Isometry Property

Mark A. Davenport·Michael B. Wakin
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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 $\delta < \frac{1}{3\sqrt{K}}$) is sufficient for OMP to exactly recover any $K$-sparse signal. Our 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.

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Mark A. Davenport, Michael B. Wakin. 2009-09-01. Analysis of Orthogonal Matching Pursuit using the Restricted Isometry Property. https://arxiv.org/abs/0909.0083

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