Joint block diagonalization algorithms for optimal separation of multidimensional components

Authors:
Dana Lahat;Jean-Fran$#231/ois Cardoso;Hagit Messer
Affiliations:
School of Electrical Engineering, Tel Aviv University, Tel Aviv, Israel;LTCI, TELECOM ParisTECH and CNRS, Paris, France;School of Electrical Engineering, Tel Aviv University, Tel Aviv, Israel
Venue:
LVA/ICA'12 Proceedings of the 10th international conference on Latent Variable Analysis and Signal Separation
Year:
2012

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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.