Asymptotically Optimal Recovery of Gaussian Sources from Noisy Stationary Mixtures: The Least-noisy Maximally-separating Solution

Amir Weiss, Arie Yeredor

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

1 Scopus citations

Abstract

We address the problem of source separation from noisy mixtures in a semi-blind scenario, with stationary, temporally-diverse Gaussian sources and known spectra. In such noisy models, a dilemma arises regarding the desired objective. On one hand, a maximally separating solution, providing the minimal attainable Interference-to-Source-Ratio (ISR), would often suffer from significant residual noise. On the other hand, optimal Minimum Mean Square Error (MMSE) estimation would yield estimates which are the least distorted versions of the true sources, often at the cost of compromised ISR. Based on Maximum Likelihood (ML) estimation of the unknown underlying model parameters, we propose two ML-based estimates of the sources. One asymptotically coincides with the MMSE estimate of the sources, whereas the other asymptotically coincides with the (unbiased) least-noisy maximally-separating solution for this model. We prove the asymptotic optimality of the latter and present the corresponding Cramér-Rao lower bound. We discuss the differences in principal properties of the proposed estimates and demonstrate them empirically using simulation results.

Original languageEnglish
Title of host publication2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5466-5470
Number of pages5
ISBN (Electronic)9781479981311
DOIs
StatePublished - May 2019
Externally publishedYes
Event44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Brighton, United Kingdom
Duration: 12 May 201917 May 2019

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2019-May
ISSN (Print)1520-6149

Conference

Conference44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019
Country/TerritoryUnited Kingdom
CityBrighton
Period12/05/1917/05/19

Bibliographical note

Publisher Copyright:
© 2019 IEEE.

Keywords

  • independent component analysis
  • least squares.
  • maximum likelihood
  • minimum mean square error
  • Semi-blind source separation

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