A kurtosis-based blind separation of sources using the Cayley transform

This paper proposes a new kurtosis-based method for blind separation of sources. For instantaneous mixture of sources, the conventional kurtosis-based approaches provide an elegant solution, where separation is made by minimizing or maximizing certain contrast functions with respect to an orthogonal matrix representing the separator. In the case of a convolutive mixture, however the class of orthogonal matrices need to be extended to that of para-unitary matrices, and its treatment becomes cumbersome. In this paper the problem is overcome by introducing the Cayley transform, which transforms a para-unitary matrix to a para-skew-Hermitian matrix. The fact that the set of para-skew-Hermitian matrices is a vector space offers a relatively simple method for kurtosis-based blind separation of convolutively mixed signals