A Bayesian derivation of generalized coherence detectors

Songsri Sirianunpiboon, Stephen D. Howard, Douglas Cochran

Research output: Chapter in Book/Report/Conference proceedingConference contribution

17 Citations (Scopus)

Abstract

The generalized coherence (GC) estimate is a well studied statistic for detection of a common but unknown signal on several noisy channels. In this paper, it is shown that the GC detector arises naturally from a Bayesian perspective. Specifically, it is derived as a test of the hypothesis that the signals in the channels are independent Gaussian processes against the hypothesis that the processes have some arbitrary correlation. This is achieved by introducing suitable non-informative priors for the covariance matrices across the channels under the two hypotheses. Subsequently, reduced likelihoods are obtained by marginalizing the joint distribution of the data and the covariance matrix in each case. The likelihood ratio is then shown to be a monotonic function of the GC detection statistic. This derivation extends to the case of time-correlated signals, allowing comparison with the generalized likelihood ratio test (GLRT) recently proposed by Ramírez et al.

Original languageEnglish (US)
Title of host publicationICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Pages3253-3256
Number of pages4
DOIs
StatePublished - 2012
Event2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 - Kyoto, Japan
Duration: Mar 25 2012Mar 30 2012

Other

Other2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012
CountryJapan
CityKyoto
Period3/25/123/30/12

Fingerprint

Covariance matrix
Detectors
Statistics

Keywords

  • Bayesian methods
  • generalized coherence estimate
  • multi-channel signal processing
  • non-informative priors

ASJC Scopus subject areas

  • Signal Processing
  • Software
  • Electrical and Electronic Engineering

Cite this

Sirianunpiboon, S., Howard, S. D., & Cochran, D. (2012). A Bayesian derivation of generalized coherence detectors. In ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings (pp. 3253-3256). [6288609] https://doi.org/10.1109/ICASSP.2012.6288609

A Bayesian derivation of generalized coherence detectors. / Sirianunpiboon, Songsri; Howard, Stephen D.; Cochran, Douglas.

ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. 2012. p. 3253-3256 6288609.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Sirianunpiboon, S, Howard, SD & Cochran, D 2012, A Bayesian derivation of generalized coherence detectors. in ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings., 6288609, pp. 3253-3256, 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012, Kyoto, Japan, 3/25/12. https://doi.org/10.1109/ICASSP.2012.6288609
Sirianunpiboon S, Howard SD, Cochran D. A Bayesian derivation of generalized coherence detectors. In ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. 2012. p. 3253-3256. 6288609 https://doi.org/10.1109/ICASSP.2012.6288609
Sirianunpiboon, Songsri ; Howard, Stephen D. ; Cochran, Douglas. / A Bayesian derivation of generalized coherence detectors. ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. 2012. pp. 3253-3256
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