COMPLEX-VALUED ICA USING SECOND 0 R D ER STAT I STI CS

In this paper we propose a novel transformation called strong-uncorrelating transform (SUT) that can he viewed as an ex- tension of the conventional whitening transform for complex ran- dom vectors. The SUT is a second order technique that can be used as a fast Independent Component Analysis (ICA) method for complex signals. It is able to separate almost all mixtures, if the sources belong to a class of complex non-circular random variables. Moreover, it can be used as a preprocessing technique in any com- plex ICA algorithm using whitening. If the sources are circular, the SUT reduces to the usual whitening transform. In other cases it reduces the computational load. Some relevant properties of the transform as well as some simulations examples are presented.

[1]  Visa Koivunen,et al.  Complex random vectors and ICA models: identifiability, uniqueness, and separability , 2005, IEEE Transactions on Information Theory.

[2]  Visa Koivunen,et al.  Identifiability, separability, and uniqueness of linear ICA models , 2004, IEEE Signal Processing Letters.

[3]  Terrence J. Sejnowski,et al.  Complex Independent Component Analysis of Frequency-Domain Electroencephalographic Data , 2003, Neural Networks.

[4]  Simone Fiori,et al.  Extended Hebbian learning for blind separation of complex-valued sources , 2003, IEEE Trans. Circuits Syst. II Express Briefs.

[5]  Andrzej Cichocki,et al.  Adaptive Blind Signal and Image Processing - Learning Algorithms and Applications , 2002 .

[6]  Andrzej Cichocki,et al.  A New Learning Algorithm for Blind Signal Separation , 1995, NIPS.

[7]  James L. Massey,et al.  Proper complex random processes with applications to information theory , 1993, IEEE Trans. Inf. Theory.

[8]  J. Cardoso,et al.  An efficient technique for the blind separation of complex sources , 1993, [1993 Proceedings] IEEE Signal Processing Workshop on Higher-Order Statistics.

[9]  Charles R. Johnson,et al.  Matrix analysis , 1985 .

[10]  E. Oja,et al.  Independent Component Analysis , 2004, IEEE Transactions on Neural Networks.

[11]  Andrzej Cichocki,et al.  Adaptive blind signal and image processing , 2002 .

[12]  Aapo Hyvärinen,et al.  A Fast Fixed-Point Algorithm for Independent Component Analysis of Complex Valued Signals , 2000, Int. J. Neural Syst..

[13]  Jean-Franois Cardoso.  High-Order Contrasts for Independent Component Analysis , 1999, Neural Computation.

[14]  Signal Processing , 1991 .