On optimal source separation based on second and fourth order cumulants

This paper addresses performance issues in the source separation problem. By drawing on the theory of optimal statistic matching, we derive new contrast functions which are optimal among those involving a given set of cumulants. In low noise, the optimal combination of a particular set of cumulants are shown to be parameter independent and can be pre-computed. We give specific examples in closed form for several choices of 2nd and 4th order cumulants. The resulting performance is investigated as a function of the SNR for non-Gaussian source signals and further compared to suboptimal approaches.