Abstract
The second-order blind identification (SOBI) algorithm (Belouchrani et al., 1997) is a classical blind source separation (BSS) algorithm for stationary sources. The weights-adjusted SOBI (WASOBI) algorithm (Yeredor 2000) proposed a reformulation of the SOBI algorithm as a weighted nonlinear least squares problem, and showed how to obtain asymptotically optimal weights, under the assumption of Gaussian Moving Average (MA) sources. In this paper, we extend the framework by showing how to obtain the (asymptotically) optimal weight matrix also for the cases of auto-regressive (AR) or ARMA Gaussian sources (of unknown parameters), bypassing the apparent need for estimation of infinitely many correlation matrices. Comparison with other algorithms, with the Cramér Rao bound and with the analytically predicted performance is presented using simulations. In particular, we show that the optimal performance can be attained with fewer estimated correlation matrices than in the Gaussian Mutual Information approach (which is also optimal in this context).
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References
Belouchrani, A., Abed-Meraim, K., Cardoso, J.-F., Moulines, E.: A blind source separation technique using second-order statistics. IEEE Trans. Signal Processing 45, 434–444 (1997)
Yeredor, A.: Blind separation of gaussian sources via second-order statistics with asymptotically optimal weigthting. IEEE Signal Processing Letters 7, 197–200 (2000)
Yeredor, A., Doron, E.: Using farther correlations to further improve the optimally-weighted sobi algorithm. In: Proc. EUSIPCO 2002 (September 2002)
Pham, D.-T., Garat, P.: Blind separation of mixture of independent sources through a quasi-maximum likelihood approach. IEEE Trans. Signal Processing 45, 1712–1725 (1997)
Pham, D.-T.: Blind separation of instantaneous mixture of sources via the gaussian mutual iformation criterion. Signal Processing 81, 855–870 (2001)
Dégerine, S., Malki, R.: Second-order blind separation of sources based on canonical partial innovations. IEEE Trans. Signal Processing 48, 629–641 (2000)
Stoica, P., Friendlander, B., Söderström, T.: Approximate maximum-likelihood approach to arma spectral estimation. Int. J. Contr. 45(4), 1281–1310 (1987)
Doron, E.: Asymptotically optimal blind separation of parametric gaussian sources. Master’s thesis, Dept. of EE-Systems, Tel-Aviv University, Israel (2003)
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© 2004 Springer-Verlag Berlin Heidelberg
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Doron, E., Yeredor, A. (2004). Asymptotically Optimal Blind Separation of Parametric Gaussian Sources. In: Puntonet, C.G., Prieto, A. (eds) Independent Component Analysis and Blind Signal Separation. ICA 2004. Lecture Notes in Computer Science, vol 3195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30110-3_50
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DOI: https://doi.org/10.1007/978-3-540-30110-3_50
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