Testing blind separability of complex Gaussian mixtures

The separation of a complex mixture based solely on second-order statistics can be achieved using the Strong Uncorrelating Transform (SUT) if and only if all sources have distinct circularity coefficients. However, in most problems we do not know the circularity coefficients, and they must be estima...

ver descrição completa

Detalhes bibliográficos
Autores: Ramírez García, David, Schreier, Peter J., Vía Rodríguez, Javier, Santamaría Caballero, Luis Ignacio|||0000-0003-0040-7436
Formato: artículo
Fecha de publicación:2014
País:España
Recursos:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/9395
Acesso em linha:http://hdl.handle.net/10902/9395
Access Level:acceso abierto
Palavra-chave:Complex independent component analysis (ICA)
Circularity coefficients
Generalized likelihood ratio test (GLRT)
Hypothesis test
Maximum likelihood (ML) estimation
Wilks' theorem
id ES_cd449a08c438d4c868c0e01bc47b9412
oai_identifier_str oai:repositorio.unican.es:10902/9395
network_acronym_str ES
network_name_str España
repository_id_str
spelling Testing blind separability of complex Gaussian mixturesRamírez García, DavidSchreier, Peter J.Vía Rodríguez, JavierSantamaría Caballero, Luis Ignacio|||0000-0003-0040-7436Complex independent component analysis (ICA)Circularity coefficientsGeneralized likelihood ratio test (GLRT)Hypothesis testMaximum likelihood (ML) estimationWilks' theoremThe separation of a complex mixture based solely on second-order statistics can be achieved using the Strong Uncorrelating Transform (SUT) if and only if all sources have distinct circularity coefficients. However, in most problems we do not know the circularity coefficients, and they must be estimated from observed data. In this work, we propose a detector, based on the generalized likelihood ratio test (GLRT), to test the separability of a complex Gaussian mixture using the SUT. For the separable case (distinct circularity coefficients), the maximum likelihood (ML) estimates are straightforward. On the other hand, for the non-separable case (at least one circularity coefficient has multiplicity greater than one), the ML estimates are much more difficult to obtain. To set the threshold, we exploit Wilks' theorem, which gives the asymptotic distribution of the GLRT under the null hypothesis. Finally, numerical simulations show the good performance of the proposed detector and the accuracy of Wilks' approximation.ElsevierUniversidad de Cantabria20142014-02-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttp://hdl.handle.net/10902/9395Signal Processing, 2014, 95, 49–57reponame:UCrea Repositorio Abierto de la Universidad de Cantabriainstname:Universidad de Cantabria (UC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Atribución-NoComercial-SinDerivadas 3.0 Españahttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:repositorio.unican.es:10902/93952026-06-02T12:39:31Z
dc.title.none.fl_str_mv Testing blind separability of complex Gaussian mixtures
title Testing blind separability of complex Gaussian mixtures
spellingShingle Testing blind separability of complex Gaussian mixtures
Ramírez García, David
Complex independent component analysis (ICA)
Circularity coefficients
Generalized likelihood ratio test (GLRT)
Hypothesis test
Maximum likelihood (ML) estimation
Wilks' theorem
title_short Testing blind separability of complex Gaussian mixtures
title_full Testing blind separability of complex Gaussian mixtures
title_fullStr Testing blind separability of complex Gaussian mixtures
title_full_unstemmed Testing blind separability of complex Gaussian mixtures
title_sort Testing blind separability of complex Gaussian mixtures
dc.creator.none.fl_str_mv Ramírez García, David
Schreier, Peter J.
Vía Rodríguez, Javier
Santamaría Caballero, Luis Ignacio|||0000-0003-0040-7436
author Ramírez García, David
author_facet Ramírez García, David
Schreier, Peter J.
Vía Rodríguez, Javier
Santamaría Caballero, Luis Ignacio|||0000-0003-0040-7436
author_role author
author2 Schreier, Peter J.
Vía Rodríguez, Javier
Santamaría Caballero, Luis Ignacio|||0000-0003-0040-7436
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Complex independent component analysis (ICA)
Circularity coefficients
Generalized likelihood ratio test (GLRT)
Hypothesis test
Maximum likelihood (ML) estimation
Wilks' theorem
topic Complex independent component analysis (ICA)
Circularity coefficients
Generalized likelihood ratio test (GLRT)
Hypothesis test
Maximum likelihood (ML) estimation
Wilks' theorem
description The separation of a complex mixture based solely on second-order statistics can be achieved using the Strong Uncorrelating Transform (SUT) if and only if all sources have distinct circularity coefficients. However, in most problems we do not know the circularity coefficients, and they must be estimated from observed data. In this work, we propose a detector, based on the generalized likelihood ratio test (GLRT), to test the separability of a complex Gaussian mixture using the SUT. For the separable case (distinct circularity coefficients), the maximum likelihood (ML) estimates are straightforward. On the other hand, for the non-separable case (at least one circularity coefficient has multiplicity greater than one), the ML estimates are much more difficult to obtain. To set the threshold, we exploit Wilks' theorem, which gives the asymptotic distribution of the GLRT under the null hypothesis. Finally, numerical simulations show the good performance of the proposed detector and the accuracy of Wilks' approximation.
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-02-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10902/9395
url http://hdl.handle.net/10902/9395
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Atribución-NoComercial-SinDerivadas 3.0 España
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Atribución-NoComercial-SinDerivadas 3.0 España
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv Signal Processing, 2014, 95, 49–57
reponame:UCrea Repositorio Abierto de la Universidad de Cantabria
instname:Universidad de Cantabria (UC)
instname_str Universidad de Cantabria (UC)
reponame_str UCrea Repositorio Abierto de la Universidad de Cantabria
collection UCrea Repositorio Abierto de la Universidad de Cantabria
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869419794822856704
score 15,301629

Registos relacionados