Abstract
The separation of synchronous sources (SSS) is a relevant problem in the analysis of electroencephalogram (EEG) and magnetoencephalogram (MEG) synchrony. Previous experimental results, using pseudo-real MEG data, showed empirically that prewhitening improves the conditioning of the SSS problem. Simulations with synthetic data also suggest that the mixing matrix is much better conditioned after whitening is performed. Unlike in Independent Component Analysis (ICA), synchronous sources can be correlated. Thus, the reasoning used to motivate whitening in ICA is not directly extendable to SSS. In this paper, we analytically derive a tight upper bound for the condition number of the equivalent mixing matrix after whitening. We also present examples with simulated data, showing the correctness of this bound on sources with sub- and super-gaussian amplitudes. These examples further illustrate the large improvements in the condition number of the mixing matrix obtained through prewhitening, thus motivating the use of prewhitening in real applications.
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
Almeida, M., Bioucas-Dias, J., Vigário, R.: Detection and separation of phase-locked subspaces with phase noise. Signal Processing (2011) (submitted)
Almeida, M., Schleimer, J.H., Bioucas-Dias, J., Vigário, R.: Source separation and clustering of phase-locked subspaces. IEEE Transactions on Neural Networks 22(9), 1419–1434 (2011)
Almeida, M., Vigario, R., Bioucas-Dias, J.: Phase locked matrix factorization. In: Proc. of the EUSIPCO Conference (2011)
Bertero, M., Boccacci, P.: Introduction to Inverse Problems in Imaging. Taylor & Francis (1998)
Canolty, R., Edwards, E., Dalal, S., Soltani, M., Nagarajan, S., Kirsch, H., Berger, M., Barbaro, N., Knight, R.: High gamma power is phase-locked to theta oscillations in human neocortex. Science 313, 1626–1628 (2006)
Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. John Wiley & Sons (2001)
Nunez, P.L., Srinivasan, R., Westdorp, A.F., Wijesinghe, R.S., Tucker, D.M., Silberstein, R.B., Cadusch, P.J.: EEG coherency I: statistics, reference electrode, volume conduction, laplacians, cortical imaging, and interpretation at multiple scales. Electroencephalography and Clinical Neurophysiology 103, 499–515 (1997)
Palva, J.M., Palva, S., Kaila, K.: Phase synchrony among neuronal oscillations in the human cortex. Journal of Neuroscience 25(15), 3962–3972 (2005)
Pikovsky, A., Rosenblum, M., Kurths, J.: Synchronization: A universal concept in nonlinear sciences. Cambridge Nonlinear Science Series. Cambridge University Press (2001)
Schoffelen, J.M., Oostenveld, R., Fries, P.: Imaging the human motor system’s beta-band synchronization during isometric contraction. NeuroImage 41, 437–447 (2008)
Uhlhaas, P.J., Singer, W.: Neural synchrony in brain disorders: Relevance for cognitive dysfunctions and pathophysiology. Neuron 52, 155–168 (2006)
Vigário, R., Särelä, J., Jousmäki, V., Hämäläinen, M., Oja, E.: Independent component approach to the analysis of EEG and MEG recordings. IEEE Trans. On Biom. Eng. 47(5), 589–593 (2000)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Almeida, M., Vigário, R., Bioucas-Dias, J. (2012). The Role of Whitening for Separation of Synchronous Sources. 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_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-28551-6_18
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)