TY - GEN

T1 - Orthogonal matching pursuit from noisy measurements

T2 - 23rd Annual Conference on Neural Information Processing Systems, NIPS 2009

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.

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M3 - Conference contribution

AN - SCOPUS:80052365596

SN - 9781615679119

T3 - Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference

SP - 540

EP - 548

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

Y2 - 7 December 2009 through 10 December 2009

ER -