Abstract
The linear BSS problem can be solved under certain conditions via a joint diagonalization approach of only two matrices. Algebraic solutions, i.e. solutions that only involve eigenvalue decompositions or singular value decompositions, are of particular interest as efficient eigensolvers exist. Success of these methods depends significantly on particular properties of the sources, such as non-stationarity, non-whiteness, non-Gaussianity, and non-circularity. In this work, we propose alternative algebraic solutions to solve the complex BSS problem, which generalize the existing approaches. For example, applicability of SUT is limited to the positive definiteness of the covariance matrix, whereas our approach allows to exploit alternative information, such as autocorrelation and pseudo-autocorrelation, to solve the complex BBS problem.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Comon, P.: Independent component analysis, a new concept? Signal Processing 36(3), 287–314 (1994)
Comon, P., Jutten, C. (eds.): Handbook of Blind Source Separation: Independent Component Analysis and Applications. Academic Press Inc. (2010)
Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. Wiley, New York (2001)
Parra, L., Sajda, P.: Blind source separation via generalized eigenvalue decomposition. The Journal of Machine Learning Research 4(7-8), 1261–1269 (2004)
Shen, H., Kleinsteuber, M.: Complex Blind Source Separation via Simultaneous Strong Uncorrelating Transform. In: Vigneron, V., Zarzoso, V., Moreau, E., Gribonval, R., Vincent, E. (eds.) LVA/ICA 2010. LNCS, vol. 6365, pp. 287–294. Springer, Heidelberg (2010)
Eriksson, J., Koivunen, V.: Complex-valued ICA using second order statistics. In: Proceedings of the 14th IEEE International Workshop on MLSP, pp. 183–191 (2004)
Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, New York (1985)
Kleinsteuber, M.: A sort-Jacobi algorithm for semisimple Lie algebras. Linear Algebra and its Applications 430(1), 155–173 (2009)
Tong, L., Liu, R.W., Soon, V.C., Huang, Y.F.: Indeterminacy and identifiability of blind identification. IEEE Transactions on Circuits and Systems 38(5), 499–509 (1991)
Pham, D.T., Cardoso, J.F.: Blind separation of instantaneous mixtures of nonstationary sources. IEEE Transactions on Signal Processing 49(9), 1837–1848 (2001)
Molgedey, L., Schuster, H.G.: Separation of a mixture of independent signals using time delayed correlations. Physical Review Letters 72(23), 3634–3637 (1994)
De Lathauwer, L., de Moor, B.: On the blind separation of non-circular sources. In: Proceedings of the 11th EUSIPCO, pp. 99–102 (2002)
Li, X.L., Adalı, T.: Blind separation of noncircular correlated sources using Gaussian entropy rate. IEEE Transactions on Signal Processing 59(6), 2969–2975 (2011)
Benedetti, R., Cragnolini, P.: On simultaneous diagonalization of one Hermitian and one symmetric form. Linear Algebra and its Applications 57, 215–226 (1984)
Amari, S.I., Cichocki, A., Yang, H.H.: A new learning algorithm for blind signal separation. In: Touretzky, D.S., Mozer, M.C., Hasselmo, M.E. (eds.) Advances in Neural Information Processing Systems, vol. 8, pp. 757–763. The MIT Press (1996)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Shen, H., Kleinsteuber, M. (2012). Algebraic Solutions to Complex Blind Source Separation. In: Theis, F., Cichocki, A., Yeredor, A., Zibulevsky, M. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2012. Lecture Notes in Computer Science, vol 7191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28551-6_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-28551-6_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28550-9
Online ISBN: 978-3-642-28551-6
eBook Packages: Computer ScienceComputer Science (R0)