Abstract
This paper deals with the problem of Blind Source Separation. Contrary to the vast majority of works, we do not assume the statistical independence between the sources and explicitly consider that they are dependent. We introduce three particular models of dependent sources and show that their cumulants have interesting properties. Based on these properties, we investigate the behaviour of classical Blind Source Separation algorithms when applied to these sources: depending on the source vector, the separation may be sucessful or some additionnal indeterminacies can be identified.
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References
Li, T.H.: Finite-alphabet information and multivariate blind deconvolution and identification of linear systems. IEEE Trans. on Information Theory 49(1), 330–337 (2003)
Comon, P.: Contrasts, independent component analysis, and blind deconvolution. Int. Journal Adapt. Control Sig. Proc. 18(3) 225–243 (April 2004) special issue on Signal Separation: Preprint: I3S Research Report RR-2003-06 (2004), http://www3.interscience.wiley.com/cgi-bin/jhome/4508
Comon, P.: Blind identification and source separation in 2×3 under-determined mixtures. IEEE Trans. Signal Processing 52(1), 11–22 (2004)
Comon, P., Grellier, O.: Non-linear inversion of underdetermined mixtures. In: Proc. of ICA 1999, Aussois, France, pp. 461–465 (January 1999)
Hyvärinen, A., Shimizu, S.: A quasi-stochastic gradient algorithm for variance-dependent component analysis. In: Kollias, S., Stafylopatis, A., Duch, W., Oja, E. (eds.) ICANN 2006. LNCS, vol. 4131, pp. 211–220. Springer, Heidelberg (2006)
Cardoso, J.F.: Multidimensional independent component analysis. In: Proc. ICASSP 1998. Seattle (1998)
Comon, P.: Independent component analysis, a new concept. Signal Processing 36(3), 287–314 (1994)
Eriksson, J., Koivunen, V.: Complex random vectors and ICA models: Identifiability, uniqueness and separability. IEEE Trans. on Information Theory 52(3), 1017–1029 (2006)
Cardoso, J.F., Souloumiac, A.: Blind beamforming for non gaussian signals. In: IEEE- Proceedings-F. vol. 140, pp. 362–370 (1993)
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Castella, M., Comon, P. (2007). Blind Separation of Instantaneous Mixtures of Dependent Sources. In: Davies, M.E., James, C.J., Abdallah, S.A., Plumbley, M.D. (eds) Independent Component Analysis and Signal Separation. ICA 2007. Lecture Notes in Computer Science, vol 4666. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74494-8_2
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DOI: https://doi.org/10.1007/978-3-540-74494-8_2
Publisher Name: Springer, Berlin, Heidelberg
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