Distribution of the Fisher information loss due to random compressed sensing

Pooria Pakrooh; Ali Pezeshki; Louis L. Scharf; Douglas Cochran; Stephen D. Howard

doi:10.1109/ACSSC.2015.7421392

Distribution of the Fisher information loss due to random compressed sensing

Pooria Pakrooh, Ali Pezeshki, Louis L. Scharf, Douglas Cochran, Stephen D. Howard

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

1 Scopus citations

Abstract

In this work, we study the impact of compressive sampling with random matrices on Fisher information and the Cramér-Rao bound (CRB) for nonlinear parameter estimation in a complex multivariate normal measurement model. We consider the class of random compression matrices whose distribution is invariant to right-unitary transformations. For this class of random compression matrices, we show that the normalized Fisher information matrix after compression has a complex matrix-variate beta distribution, which is independent of the Fisher information matrix before compression and the values of the parameters. We also derive the distribution of CRB. Our results can be used to quantify the amount of loss in Fisher information and the increase in CRB due to random compression.

Original language	English (US)
Title of host publication	Conference Record of the 49th Asilomar Conference on Signals, Systems and Computers, ACSSC 2015
Editors	Michael B. Matthews
Publisher	IEEE Computer Society
Pages	1487-1489
Number of pages	3
ISBN (Electronic)	9781467385763
DOIs	https://doi.org/10.1109/ACSSC.2015.7421392
State	Published - Feb 26 2016
Event	49th Asilomar Conference on Signals, Systems and Computers, ACSSC 2015 - Pacific Grove, United States Duration: Nov 8 2015 → Nov 11 2015

Publication series

Name	Conference Record - Asilomar Conference on Signals, Systems and Computers
Volume	2016-February
ISSN (Print)	1058-6393

Other

Other	49th Asilomar Conference on Signals, Systems and Computers, ACSSC 2015
Country/Territory	United States
City	Pacific Grove
Period	11/8/15 → 11/11/15

ASJC Scopus subject areas

Signal Processing
Computer Networks and Communications

Access to Document

10.1109/ACSSC.2015.7421392

Cite this

Pakrooh, P., Pezeshki, A., Scharf, L. L., Cochran, D., & Howard, S. D. (2016). Distribution of the Fisher information loss due to random compressed sensing. In M. B. Matthews (Ed.), Conference Record of the 49th Asilomar Conference on Signals, Systems and Computers, ACSSC 2015 (pp. 1487-1489). Article 7421392 (Conference Record - Asilomar Conference on Signals, Systems and Computers; Vol. 2016-February). IEEE Computer Society. https://doi.org/10.1109/ACSSC.2015.7421392

Distribution of the Fisher information loss due to random compressed sensing. / Pakrooh, Pooria; Pezeshki, Ali; Scharf, Louis L. et al.
Conference Record of the 49th Asilomar Conference on Signals, Systems and Computers, ACSSC 2015. ed. / Michael B. Matthews. IEEE Computer Society, 2016. p. 1487-1489 7421392 (Conference Record - Asilomar Conference on Signals, Systems and Computers; Vol. 2016-February).

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

Pakrooh, P, Pezeshki, A, Scharf, LL, Cochran, D & Howard, SD 2016, Distribution of the Fisher information loss due to random compressed sensing. in MB Matthews (ed.), Conference Record of the 49th Asilomar Conference on Signals, Systems and Computers, ACSSC 2015., 7421392, Conference Record - Asilomar Conference on Signals, Systems and Computers, vol. 2016-February, IEEE Computer Society, pp. 1487-1489, 49th Asilomar Conference on Signals, Systems and Computers, ACSSC 2015, Pacific Grove, United States, 11/8/15. https://doi.org/10.1109/ACSSC.2015.7421392

Pakrooh P, Pezeshki A, Scharf LL, Cochran D, Howard SD. Distribution of the Fisher information loss due to random compressed sensing. In Matthews MB, editor, Conference Record of the 49th Asilomar Conference on Signals, Systems and Computers, ACSSC 2015. IEEE Computer Society. 2016. p. 1487-1489. 7421392. (Conference Record - Asilomar Conference on Signals, Systems and Computers). doi: 10.1109/ACSSC.2015.7421392

Pakrooh, Pooria ; Pezeshki, Ali ; Scharf, Louis L. et al. / Distribution of the Fisher information loss due to random compressed sensing. Conference Record of the 49th Asilomar Conference on Signals, Systems and Computers, ACSSC 2015. editor / Michael B. Matthews. IEEE Computer Society, 2016. pp. 1487-1489 (Conference Record - Asilomar Conference on Signals, Systems and Computers).

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AB - In this work, we study the impact of compressive sampling with random matrices on Fisher information and the Cramér-Rao bound (CRB) for nonlinear parameter estimation in a complex multivariate normal measurement model. We consider the class of random compression matrices whose distribution is invariant to right-unitary transformations. For this class of random compression matrices, we show that the normalized Fisher information matrix after compression has a complex matrix-variate beta distribution, which is independent of the Fisher information matrix before compression and the values of the parameters. We also derive the distribution of CRB. Our results can be used to quantify the amount of loss in Fisher information and the increase in CRB due to random compression.

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Distribution of the Fisher information loss due to random compressed sensing

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