Abstract
Traditionally, the strong uncorrelating transformation (SUT) is applied to the zero-lag sample autocovariance and pseudo- autocovariance matrices of the observed mixtures for separating complex-valued stationary sources. The performance of the SUT in that context has been recently analyzed. In this work we extend the analysis to the case where the SUT is applied to “generalized” covariance and pseudo-covariance matrices - which are prescribed by an arbitrary symmetric, positive definite matrix, termed an “association matrix”. The analysis applies not only to stationary sources, but also to sources with arbitrary complex-valued temporal covariance and pseudo-covariance. As we show, the use of generalized covariance and pseudo-covariance matrices for the SUT entails a potential for significant improvement in the resulting separation performance, as we also demonstrate in simulation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Yeredor, A.: Performance analysis of the strong uncorrelating transformation in blind separation of complex-valued sources. To Appear in IEEE Transactions on Signal Processing (2012)
Eriksson, J., Koivunen, V.: Complex random vectors and ICA models: Identifiability, uniqueness, and separability. IEEE Transactions on Information Theory 52(3), 1017–1029 (2006)
Schreier, P., Scharf, L.: Statistical Signal Processing of Complex-valued Data. Cambridge University Press (2010)
Benedetti, R., Cragnolini, P.: On simultaneous diagonalization of one Hermitian and one symmetric form. Linear Algebra and its Applications 57, 215–226 (1984)
De Lathauwer, L., De Moor, B.: On the blind separation of non-circular sources. In: XIth European Signal Processing Conf. (EUSIPCO 2002), pp. 99–102 (September 2002)
Eriksson, J., Koivunen, V.: Complex-valued ICA using second order statistics. In: Proceedings of the 2004 IEEE Machine Learning for Signal Processing Workshop XIV, pp. 183–191 (2004)
Horn, R., Johnson, C.: Matrix Analysis. Cambridge University Press (1985)
Ollila, E., Koivunen, V.: Complex ICA using generalized uncorrelating transform. Signal Processing 89(4), 365–377 (2009)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yeredor, A. (2012). On the Separation Performance of the Strong Uncorrelating Transformation When Applied to Generalized Covariance and Pseudo-covariance Matrices. 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_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-28551-6_11
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)