Orthogonal Matching Pursuit for Sparse Signal Recovery With Noise
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Wang_Orthogonal Matching.pdf
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Author(s)
Cai, T. Tony
Wang, Lie
Date Issued
July 2011
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers
Citation
Cai, T. Tony, and Lie Wang. “Orthogonal Matching Pursuit for Sparse Signal Recovery With Noise.” IEEE Transactions on Information Theory 57.7 (2011): 4680–4688.
Version
Author's final manuscript
Abstract
We consider the orthogonal matching pursuit (OMP) algorithm for the recovery of a high-dimensional sparse signal based on a small number of noisy linear measurements. OMP is an iterative greedy algorithm that selects at each step the column, which is most correlated with the current residuals. In this paper, we present a fully data driven OMP algorithm with explicit stopping rules. It is shown that under conditions on the mutual incoherence and the minimum magnitude of the nonzero components of the signal, the support of the signal can be recovered exactly by the OMP algorithm with high probability. In addition, we also consider the problem of identifying significant components in the case where some of the nonzero components are possibly small. It is shown that in this case the OMP algorithm will still select all the significant components before possibly selecting incorrect ones. Moreover, with modified stopping rules, the OMP algorithm can ensure that no zero components are selected.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1109/tit.2011.2146090
