Abstract
This paper deals with non-orthogonal joint block diagonalization. Two algorithms which minimize the Kullback-Leibler divergence between a set of real positive-definite matrices and a block-diagonal transformation thereof are suggested. One algorithm is based on the relative gradient, and the other is based on a quasi-Newton method. These algorithms allow for the optimal, in the mean square error sense, blind separation of multidimensional Gaussian components. Simulations demonstrate the convergence properties of the suggested algorithms, as well as the dependence of the criterion on some of the model parameters.
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References
Nion, D.: A tensor framework for nonunitary joint block diagonalization. IEEE Trans. Signal Process. 59(10), 4585–4594 (2011)
Ghennioui, H., et al.: Gradient-based joint block diagonalization algorithms: Application to blind separation of FIR convolutive mixtures. Signal Process. 90(6), 1836–1849 (2010)
Bousbia-Salah, H., Belouchrani, A., Abed-Meraim, K.: Blind separation of non stationary sources using joint block diagonalization. In: Proc. SSP, pp. 448–451 (August 2001)
Pham, D.-T.: Joint approximate diagonalization of positive definite hermitian matrices. SIAM J. Matrix Anal. Appl. 22(4), 1136–1152 (2001)
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)
Lahat, D., Cardoso, J.-F., Messer, H.: Second-order multidimensional ICA: Performance analysis. Submitted to IEEE. Trans. Sig. Proc. (September 2011)
Comon, P.: Independent component analysis. In: Proc. Int. Signal Process. Workshop on HOS, Chamrousse, France, pp. 111–120 (July 1991); keynote address. Republished in HOS, J.-L. Lacoume ed., Elsevier, 1992, pp. 29–38
Pham, D.-T., Cardoso, J.-F.: Blind separation of instantaneous mixtures of non stationary sources. IEEE Trans. Signal Process. 49(9), 1837–1848 (2001)
Cardoso, J.-F., Laheld, B.: Equivariant adaptive source separation. IEEE Trans. Signal Process. 44(12), 3017–3030 (1996)
Pham, D.-T.: Information approach to blind source separation and deconvolution. In: Emmert-Streib, F., Dehmer, M. (eds.) Information Theory and Statistical Learning, ch.7, pp. 153–182. Springer, Heidelberg (2009)
Graham, A.: Kronecker Products and Matrix Calculus with Applications. Mathematics and its Applications. Ellis Horwood Ltd., Chichester (1981)
Gutch, H.W., Maehara, T., Theis, F.J.: Second Order Subspace Analysis and Simple Decompositions. In: Vigneron, V., Zarzoso, V., Moreau, E., Gribonval, R., Vincent, E. (eds.) LVA/ICA 2010. LNCS, vol. 6365, pp. 370–377. Springer, Heidelberg (2010)
Vía, J., et al.: A Maximum Likelihood approach for Independent Vector Analysis of Gaussian data sets. In: Proc. MLSP 2011, Beijing, China (September 2011)
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Lahat, D., Cardoso, JF., Messer, H. (2012). Joint Block Diagonalization Algorithms for Optimal Separation of Multidimensional Components. 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_20
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DOI: https://doi.org/10.1007/978-3-642-28551-6_20
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