On consistency and asymptotic uniqueness in quasi-maximum likelihood blind separation of temporally-diverse sources

Amir Weiss, Arie Yeredor, Sher Ali Cheema, Martin Haardt

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

1 Scopus citations

Abstract

In its basic, fully blind form, Independent Component Analysis (ICA) does not rely on a particular statistical model of the sources, but only on their mutual statistical independence, and therefore does not admit a Maximum Likelihood (ML) estimation framework. In semi-blind scenarios statistical models of the sources are available, enabling ML separation. Quasi-ML (QML) methods operate in the (more realistic) fully-blind scenarios, simply by presuming some hypothesized statistical models, thereby obtaining QML separation. When these models are (or are assumed to be) Gaussian with distinct temporal covariance matrices, the (quasi-)likelihood equations take the form of a 'Sequentially Drilled Joint Congruence' (SeDJoCo) transformation problem. In this work we state some mild conditions on the sources' true and presumed covariance matrices, which guarantee consistency of the QML separation when the SeDJoCo solution is asymptotically unique. In addition, we derive a necessary 'Mutual Diversity' condition on these matrices for the asymptotic uniqueness of the SeDJoCo solution. Finally, we demonstrate the consistency of QML in various simulation scenarios.

Original languageEnglish
Title of host publication2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4459-4463
Number of pages5
ISBN (Print)9781538646588
DOIs
StatePublished - 10 Sep 2018
Externally publishedYes
Event2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Calgary, Canada
Duration: 15 Apr 201820 Apr 2018

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2018-April
ISSN (Print)1520-6149

Conference

Conference2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018
Country/TerritoryCanada
CityCalgary
Period15/04/1820/04/18

Bibliographical note

Publisher Copyright:
© 2018 IEEE.

Keywords

  • Blind source separation
  • Consistency
  • Quasi-maximum likelihood
  • SeDJoCo

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