### Abstract

A well-known analysis of Tropp and Gilbert shows that orthogonal matching pursuit (OMP) can recover a k-sparse n-dimensional real vector from m = 4k log(n) noise-free linear measurements obtained through a random Gaussian measurement matrix with a probability that approaches one as n → ∞. This work strengthens this result by showing that a lower number of measurements, m = 2klog(n - k), is in fact sufficient for asymptotic recovery. More generally, when the sparsity level satisfies k
_{min} ≤ k ≤ k
_{max} but is unknown, m = 2k
_{max}log(n - k
_{min}) measurements is sufficient. Furthermore, this number of measurements is also sufficient for detection of the sparsity pattern (support) of the vector with measurement errors provided the signal-to-noise ratio (SNR) scales to infinity. The scaling m = 2k log(n - k) exactly matches the number of measurements required by the more complex lasso method for signal recovery in a similar SNR scaling.

Original language | English (US) |
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Title of host publication | Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference |

Pages | 540-548 |

Number of pages | 9 |

State | Published - 2009 |

Event | 23rd Annual Conference on Neural Information Processing Systems, NIPS 2009 - Vancouver, BC, Canada Duration: Dec 7 2009 → Dec 10 2009 |

### Other

Other | 23rd Annual Conference on Neural Information Processing Systems, NIPS 2009 |
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Country | Canada |

City | Vancouver, BC |

Period | 12/7/09 → 12/10/09 |

### Fingerprint

### ASJC Scopus subject areas

- Information Systems

### Cite this

*Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference*(pp. 540-548)

**Orthogonal matching pursuit from noisy measurements : A new analysis.** / Fletcher, Alyson K.; Rangan, Sundeep.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference.*pp. 540-548, 23rd Annual Conference on Neural Information Processing Systems, NIPS 2009, Vancouver, BC, Canada, 12/7/09.

}

TY - GEN

T1 - Orthogonal matching pursuit from noisy measurements

T2 - A new analysis

AU - Fletcher, Alyson K.

AU - Rangan, Sundeep

PY - 2009

Y1 - 2009

N2 - A well-known analysis of Tropp and Gilbert shows that orthogonal matching pursuit (OMP) can recover a k-sparse n-dimensional real vector from m = 4k log(n) noise-free linear measurements obtained through a random Gaussian measurement matrix with a probability that approaches one as n → ∞. This work strengthens this result by showing that a lower number of measurements, m = 2klog(n - k), is in fact sufficient for asymptotic recovery. More generally, when the sparsity level satisfies k min ≤ k ≤ k max but is unknown, m = 2k maxlog(n - k min) measurements is sufficient. Furthermore, this number of measurements is also sufficient for detection of the sparsity pattern (support) of the vector with measurement errors provided the signal-to-noise ratio (SNR) scales to infinity. The scaling m = 2k log(n - k) exactly matches the number of measurements required by the more complex lasso method for signal recovery in a similar SNR scaling.

AB - A well-known analysis of Tropp and Gilbert shows that orthogonal matching pursuit (OMP) can recover a k-sparse n-dimensional real vector from m = 4k log(n) noise-free linear measurements obtained through a random Gaussian measurement matrix with a probability that approaches one as n → ∞. This work strengthens this result by showing that a lower number of measurements, m = 2klog(n - k), is in fact sufficient for asymptotic recovery. More generally, when the sparsity level satisfies k min ≤ k ≤ k max but is unknown, m = 2k maxlog(n - k min) measurements is sufficient. Furthermore, this number of measurements is also sufficient for detection of the sparsity pattern (support) of the vector with measurement errors provided the signal-to-noise ratio (SNR) scales to infinity. The scaling m = 2k log(n - k) exactly matches the number of measurements required by the more complex lasso method for signal recovery in a similar SNR scaling.

UR - http://www.scopus.com/inward/record.url?scp=80052365596&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052365596&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:80052365596

SN - 9781615679119

SP - 540

EP - 548

BT - Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference

ER -