Strong consistency of the over- and under-determined LSE of 2-D exponentials in white noise

Joseph M. Francos, Mark Kliger

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

We consider the problem of least squares estimation of the parameters of 2-D exponential signals observed in the presence of an additive noise field, when the assumed number of exponentials is incorrect. We consider both the case where the number of exponential signals is under-estimated, and the case where the number of exponential signals is over-estimated. In the case where the number of exponential signals is under-estimated we prove the almost sure convergence of the least squares estimates to the parameters of the dominant exponentials. In the case where the number of exponential signals is over-estimated, the estimated parameter vector obtained by the least squares estimator contains a sub-vector that converges almost surely to the correct parameters of the exponentials.

Original languageEnglish
Title of host publication2005 IEEE ICASSP '05 - Proc. - Design and Implementation of Signal Proces.Syst.,Indust. Technol. Track,Machine Learning for Signal Proces. Signal Proces. Education, Spec. Sessions
PublisherInstitute of Electrical and Electronics Engineers Inc.
PagesIV669-IV672
ISBN (Print)0780388747, 9780780388741
DOIs
StatePublished - 1 Jan 2005
Event2005 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '05 - Philadelphia, PA, United States
Duration: 18 Mar 200523 Mar 2005

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
VolumeIV
ISSN (Print)1520-6149

Conference

Conference2005 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '05
Country/TerritoryUnited States
CityPhiladelphia, PA
Period18/03/0523/03/05

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