Blind Identification Of Independent Components With Higher-order Statistics

We consider a N-variate random process consisting in N (or less) independent components corrupted by additive noise. Identifying (or separating) these components without any a-priori information about their structure (blind identification) is theorically possible under the independence assumption. We propose a blind algorithm based on second- and fourth-order statistics. Its main feature is the use of tensor formalism allowing blind identification to be performed as a generalized eigen-decomposition of the "quadricovariance tensor". All non-Gaussian components (and possibly one Gaussian component) are separated even if they have identical probability distributions. Simulations in Array Processing context are included.