Blind source separation of convolutive mixtures by maximization of fourth-order cumulants: the non i.i.d. case

We address the problem of the separation of convolutive mixtures in the case where the non-Gaussian source signals are not necessarily filtered versions of i.i.d. sequences. In this context, we study the behavior of the schemes based on the maximization of a fourth-order cumulant based contrast function, which are known to be consistent if the source signals are filtered versions of i.i.d. sequences. We first address the non-iterative separation approach sketched recently by Comon and Moreau (see IEEE SP Letters, vol.3, no.7, p.209-21, 1996) and Pesquet (see IEEE SP Letters, vol.4, no.6, p.182-83, 1996), and explain why it seems questionable in the non i.i.d. source signals case. Next, we show that if the sources are extracted iteratively, then the maximization of the absolute value of the fourth-order cumulant allows to separate the sources in the non i.i.d. case. We finally establish that, as in the i.i.d. case, this contrast function is free of spurious local maximum.