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Asymptotic achievability of the Cramér-Rao bound for noisy compressive sampling

Publication ,  Journal Article
Babadi, B; Kalouptsidis, N; Tarokh, V
Published in: IEEE Transactions on Signal Processing
January 1, 2009

We consider a model of the form =Ax + n, where x ε CM is sparse with at most L nonzero coefficients in unknown locations, y ε CN is the observation vector, A CN×M is the measurement matrix and n ε CN is the Gaussian noise. We develop a Cramér-Rao bound on the mean squared estimation error of the nonzero elements of x, corresponding to the genie-aided estimator (GAE) which is provided with the locations of the nonzero elements of x. Intuitively, the mean squared estimation error of any estimator without the knowledge of the locations of the nonzero elements of x is no less than that of the GAE. Assuming that L/N is fixed, we establish the existence of an estimator that asymptotically achieves the Cramér-Rao bound without any knowledge of the locations of the nonzero elements of x as N → infinite;, for Aa random Gaussian matrix whose elements are drawn i.i.d. according to N (0,1). © 2009 IEEE.

Duke Scholars

Published In

IEEE Transactions on Signal Processing

DOI

ISSN

1053-587X

Publication Date

January 1, 2009

Volume

57

Issue

3

Start / End Page

1233 / 1236

Related Subject Headings

  • Networking & Telecommunications
 

Citation

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Babadi, B., Kalouptsidis, N., & Tarokh, V. (2009). Asymptotic achievability of the Cramér-Rao bound for noisy compressive sampling. IEEE Transactions on Signal Processing, 57(3), 1233–1236. https://doi.org/10.1109/TSP.2008.2010379
Babadi, B., N. Kalouptsidis, and V. Tarokh. “Asymptotic achievability of the Cramér-Rao bound for noisy compressive sampling.” IEEE Transactions on Signal Processing 57, no. 3 (January 1, 2009): 1233–36. https://doi.org/10.1109/TSP.2008.2010379.
Babadi B, Kalouptsidis N, Tarokh V. Asymptotic achievability of the Cramér-Rao bound for noisy compressive sampling. IEEE Transactions on Signal Processing. 2009 Jan 1;57(3):1233–6.
Babadi, B., et al. “Asymptotic achievability of the Cramér-Rao bound for noisy compressive sampling.” IEEE Transactions on Signal Processing, vol. 57, no. 3, Jan. 2009, pp. 1233–36. Scopus, doi:10.1109/TSP.2008.2010379.
Babadi B, Kalouptsidis N, Tarokh V. Asymptotic achievability of the Cramér-Rao bound for noisy compressive sampling. IEEE Transactions on Signal Processing. 2009 Jan 1;57(3):1233–1236.

Published In

IEEE Transactions on Signal Processing

DOI

ISSN

1053-587X

Publication Date

January 1, 2009

Volume

57

Issue

3

Start / End Page

1233 / 1236

Related Subject Headings

  • Networking & Telecommunications