Abstract
This paper focuses on the second order identifiability problem of blind source separation and its testing. We present first necessary and sufficient conditions for the identifiability and partial identifiability using a finite set of correlation matrices. These conditions depend on the autocorrelation fonction of the unknown sources. However, it is shown here that they can be tested directly from the observation through the decorrelator output. This issue is of prime importance to decide whether the sources have been well separated or else if further treatments are needed. We then propose an identifiability testing based on resampling (jackknife) technique, that is validated by simulation results.
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References
Nandi, A.K. (ed.): Blind estimation using higher-order statistics. Kluwer Acadimic Publishers, Boston (1999)
Pham, D.T., Cardoso, J.: Blind source separation of instantaneous mixtures of nonstationary sources. IEEE Trans. SP. 49(9), 1837–1848 (2001)
Abed-Meraim, K., Xiang, Y., Hua, Y.: Generalized second order identifiability condition and relevant testing technique. In: Proc. ICASSP, vol. 5, pp. 2989–2992 (2000)
Tong, L., Liu, R., Soon, V.C., Huang, Y.H.: Indeterminacy and identifiability of blind identification. IEEE-T-CS 38, 499–509 (1991)
Belouchrani, A., Abed-Meraim, K., Cardoso, J.F., Moulines, E.: Blind source separation using second order statistics. IEEE Trans. SP, 434–444 (1997)
Kawamoto, M., Matsuoka, K., Oya, M.: Blind separation of sources using temporal correlation of the observed signal. IEICE Tr. on Fundamentals of Electronics Communications and Computing E80 A(4), 695–704 (1997)
Abed-Meraim, K., Hua, Y., Belouchrani, A.: A general framework for blind source separation using second order statistics. In: Eighth IEEE Digital Signal Processing Workshop, Utah, USA (CD-ROM) (August 1998)
Zoubir, A.M., Boashash, B.: The bootstrap and its application in signal processing. IEEE Signal Processing Magazine 15, 56–76 (1998)
Efron, B.: The jackknife, the bootstrap and other resampling plans. CBMS Monograph 38, Society for Industrial and Applied Mathematics, Philadelphia (1982)
Miller, R.G.: The jackknife - A review. Biometrika 61, 1–15 (1974)
Belouchrani, A., Amin, M.G., Chenshu Wang, M.G.: Interference mitigation in spread spectrum communications using blind source separation. In: Asilomar Conference, pp. 718–719 (1996)
D’Urso, G., Prieur, P., Vincent, C.: Blind identification methods applied to Electricite de France’s civil works and power plants monitoring. In: Higher-Order Statistics. Proceedings of the IEEE Signal Processing Workshop, pp. 82–86 (1997)
Cardoso, J.F., Souloumiac, A.: A.Blind beamforming for non-Gaussian signals. Radar and Signal Processing, IEE Proceedings F 140, 362–370 (1993)
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© 2006 Springer-Verlag Berlin Heidelberg
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Aïssa-El-Bey, A., Abed-Meraim, K., Grenier, Y. (2006). On the Identifiability Testing in Blind Source Separation Using Resampling Technique. In: Rosca, J., Erdogmus, D., Príncipe, J.C., Haykin, S. (eds) Independent Component Analysis and Blind Signal Separation. ICA 2006. Lecture Notes in Computer Science, vol 3889. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11679363_94
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DOI: https://doi.org/10.1007/11679363_94
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-32630-4
Online ISBN: 978-3-540-32631-1
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