Blind Separation of Noisy Multivariate Data Using Second-Order Statistics

A second-order method for blind source separation of noisy instantaneous linear mix-tures is presented and analyzed for the case where the signal order k and noise co-variance GGH are unknown. Only a data set X of dimension n> k and of sample size m is observed, where X = AP + GW. The quality of separation depends on source-observation ratio}, the degree of spectral diversity, and the second-order non-stationarity of the underlying sources. The algorithm estimates the Second-Order separation transform A, the signal Order, and Noise, and is therefore referred to as SOON. SOON iteratively estimates: 1) k using a scree metric, and 2) the values of AP, G, and W using the Expectation-Maximization (EM) algorithm, where W is white noise and G is diagonal. The final step estimates A and the set of k under-lying sources P using a variant of the joint diagonalization method, where P has k independent unit-variance elements. Tests using simulated Auto Regressive (AR) gaussian data show that SOON im-proves the quality of source separation in comparison to the standard second-orde