A Bayesian derivation of generalized coherence detectors

Songsri Sirianunpiboon, Stephen D. Howard, Douglas Cochran

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

18 Scopus citations

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 publication2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 - Proceedings
Pages3253-3256
Number of pages4
DOIs
StatePublished - Oct 23 2012
Event2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 - Kyoto, Japan
Duration: Mar 25 2012Mar 30 2012

Publication series

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

Other

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

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Keywords

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

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

Cite this

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