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 proceedingConference 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 languageEnglish (US)
Title of host publicationConference Record - Asilomar Conference on Signals, Systems and Computers
PublisherIEEE Computer Society
Pages1487-1489
Number of pages3
Volume2016-February
ISBN (Print)9781467385763
DOIs
StatePublished - Feb 26 2016
Event49th Asilomar Conference on Signals, Systems and Computers, ACSSC 2015 - Pacific Grove, United States
Duration: Nov 8 2015Nov 11 2015

Other

Other49th Asilomar Conference on Signals, Systems and Computers, ACSSC 2015
CountryUnited States
CityPacific Grove
Period11/8/1511/11/15

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Signal Processing

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  • 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 Conference Record - Asilomar Conference on Signals, Systems and Computers (Vol. 2016-February, pp. 1487-1489). [7421392] IEEE Computer Society. https://doi.org/10.1109/ACSSC.2015.7421392