A general framework for second-order blind separation of stationary colored sources

Bey, Abdeldjalil Aïssa El; Abed-Meraim, Karim; Grenier, Yves; Hua, Yingbo

doi:10.1016/j.sigpro.2008.03.017

Cited by 11 publications

(4 citation statements)

References 23 publications

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“…Pioneering works in [26,27] show that real valued source signals with distinct spectral density functions are blindly identifiable by using only the autocorrelation of the observations. Similar results in [28] show that stationary colored complex signals can be blindly separated by using a set of autocorrelation matrices. When source signals are both stationary and white, it requires more knowledge about the signals, such as higher-order statistics [14].…”

Section: Introductionsupporting

confidence: 63%

Uniqueness Analysis of Non-Unitary Matrix Joint Diagonalization

Kleinsteuber

Shen

2013

IEEE Trans. Signal Process.

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Matrix Joint Diagonalization (MJD) is a powerful approach for solving the Blind Source Separation (BSS) problem. It relies on the construction of matrices which are diagonalized by the unknown demixing matrix. Their joint diagonalizer serves as a correct estimate of this demixing matrix only if it is uniquely determined. Thus, a critical question is under what conditions a joint diagonalizer is unique. In the present work we fully answer this question about the identifiability of MJD based BSS approaches and provide a general result on uniqueness conditions of matrix joint diagonalization. It unifies all existing results which exploit the concepts of non-circularity, non-stationarity, non-whiteness, and non-Gaussianity. As a corollary, we propose a solution for complex BSS, which can be formulated in a closed form in terms of an eigenvalue and a singular value decomposition of two matrices.

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Section: Introductionsupporting

confidence: 63%

Uniqueness Analysis of Non-Unitary Matrix Joint Diagonalization

Kleinsteuber

Shen

2013

IEEE Trans. Signal Process.

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“…uniqueness of the solution up to the inherent problem ambiguities [18]) of the considered AR mixture model followed by a discussion on the algorithm's behavior when the AR order p is misestimated. …”

Section: Identifiability Resultsmentioning

confidence: 99%

“…The proof can be inspired from the identifiability results in [18]. Note that if two sources s i and s j have the same AR coefficients, i.e.…”

Section: Identifiability Resultsmentioning

confidence: 99%

Separation of Dependent Autoregressive Sources Using Joint Matrix Diagonalization

Boudjellal

Mesloub

Abed-Meraim

et al. 2015

IEEE Signal Process. Lett.

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This letter proposes a novel technique for the blind separation of autoregressive (AR) sources. The latter relies on the joint diagonalization (JD) of appropriate AR matrix coefficients of the observed signals and can be applied to the separation of statistically dependent sources. The developed algorithm is referred to as 'DARSS-JD' (for Dependent AR Source Separation using JD). Through the simulation experiments, DARSS-JD is shown to overcome existing second order separation methods with a relatively moderate computational cost.

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“…They are those changes, when available, that provide enough information to solve the BSS problem. Formally, for AJDC the identifiability of sources discussed above, that is, matching condition (8.3), is described by the fundamental AJD-based BSS theorem (Afsari, 2008; see also Aïssa- El-Bey et al, 2008): let matrices S 1 , S 2 ,.. be the K (unknown) covariance matrices of sources corresponding to the covariance matrices included in the diagonalization set and s k(ij) their elements. The diagonal elements of these matrices s k(ii) hold the source variance.…”

Section: Approximate Joint Diagonalization Of Covariance Matrices (Ajdc)mentioning

confidence: 99%

An Introduction to EEG Source Analysis with an Illustration of a Study on Error-Related Potentials

Congedo

Rousseau

Jutten

2014

Guide to Brain-Computer Music Interfacing

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A general framework for second-order blind separation of stationary colored sources

Cited by 11 publications

References 23 publications

Uniqueness Analysis of Non-Unitary Matrix Joint Diagonalization

Uniqueness Analysis of Non-Unitary Matrix Joint Diagonalization

Separation of Dependent Autoregressive Sources Using Joint Matrix Diagonalization

An Introduction to EEG Source Analysis with an Illustration of a Study on Error-Related Potentials

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