Abstract
Independent component analysis (ICA) and blind source separation (BSS) deal with extracting mutually-independent elements from their observed mixtures. In “classical” ICA, each component is one-dimensional in the sense that it is proportional to a column of the mixing matrix. However, this paper considers a more general setup, of multidimensional components. In terms of the underlying sources, this means that the source covariance matrix is block-diagonal rather than diagonal, so that sources belonging to the same block are correlated whereas sources belonging to different blocks are uncorrelated. These two points of view —correlated sources vs. multidimensional components— are considered in this paper. The latter offers the benefit of providing a unique decomposition. We present a novel, closed-form expression for the optimal performance of second-order ICA in the case of multidimensional elements. Our analysis is verified through numerical experiments.
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References
Abed-Meraim, K., Belouchrani, A.: Algorithms for joint block diagonalization. In: Proceedings of EUSIPCO 2004, Vienna, Austria, pp. 209–212 (2004)
Bousbia-Salah, H., Belouchrani, A., Abed-Meraim, K.: Blind separation of convolutive mixtures using joint block diagonalization. In: Sixth International Symposium on Signal Processing and its Applications, vol. 1, pp. 13–16 (August 2001)
Cardoso, J.-F.: Multidimensional independent component analysis. In: Proc. IEEE International Conference on Acoustics, Speech and Signal Processing, 12-15 May, vol. 4, pp. 1941–1944 (1998)
Cardoso, J.-F., Martin, M., Delabrouille, J., Betoule, M., Patanchon, G.: Component separation with flexible models. Application to the separation of astrophysical emissions. In: IEEE J-STSP. Special Issue on: Signal Processing for Astronomical and Space Research Applications (October 2008), http://arxiv.org/abs/0803.1814
Févotte, C., Theis, F.J.: Pivot selection strategies in jacobi joint block-diagonalization. In: Davies, M.E., James, C.J., Abdallah, S.A., Plumbley, M.D. (eds.) ICA 2007. LNCS, vol. 4666, pp. 177–184. Springer, Heidelberg (2007)
Ghennioui, H., El Mostafa, F., Thirion-Moreau, N., Adib, A., Moreau, E.: A nonunitary joint block diagonalization algorithm for blind separation of convolutive mixtures of sources. Signal Processing Letters, IEEE 14(11), 860–863 (2007)
Lahat, D., Cardoso, J.-F., Messer, H.: Multidimensional ICA: Second-order methods and applications (in preparation)
Ossadtchi, A., Baillet, S., Mosher, J.C., Thyerlei, D., Sutherling, W., Leahy, R.M.: Automated interictal spike detection and source localization in magnetoencephalography using independent components analysis and spatio-temporal clustering. Clin. Neurophysiol. 115(3), 508–522 (2004)
Pham, D.T.: Blind separation of cyclostationary sources using joint block approximate diagonalization. In: Davies, M.E., James, C.J., Abdallah, S.A., Plumbley, M.D. (eds.) ICA 2007. LNCS, vol. 4666, pp. 244–251. Springer, Heidelberg (2007)
Pham, D.-T., Cardoso, J.-F.: Blind separation of instantaneous mixtures of non stationary sources. IEEE Trans. Sig. Proc. 49(9), 1837–1848 (2001)
Pham, D.-T., Garat, P.: Blind separation of mixtures of independent sources through a quasi- maximum likelihood approach. IEEE Trans. Sig. Proc. 45(7), 1712–1725 (1997)
Vollgraf, R., Obermayer, K.: Multi-dimensional ICA to separate correlated sources. In: Neural Information Processing Systems (NIPS 2001), vol. 14, pp. 993–1000. MIT Press, Cambridge (2001)
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Lahat, D., Cardoso, JF., Messer, H. (2009). Optimal Performance of Second-Order Multidimensional ICA. In: Adali, T., Jutten, C., Romano, J.M.T., Barros, A.K. (eds) Independent Component Analysis and Signal Separation. ICA 2009. Lecture Notes in Computer Science, vol 5441. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00599-2_7
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DOI: https://doi.org/10.1007/978-3-642-00599-2_7
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