Blind separation of noisy multivariate data using second-order statistics

摘要

A second-order method for blind source separation of noisy instantaneous linear mixtures is presented and analyzed for the case where the signal order k and noise covariance GG-H 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 k/n, 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 underlying 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 improves the quality of source separation in comparison to the standard second-order separation algorithms, i.e., Second-Order Blind Identification (SOBI) [3] and Second-Order Non-Stationary (SONS) blind identification [4]. The sensitivity in performance of SONS and SOON to several algorithmic parameters is also displayed in these experiments. To reduce sensitivities in the pre-whitening step of these algorithms, a heuristic is proposed by this thesis for whitening the data set; it is shown to improve separation performance. Additionally the application of blind source separation techniques to remote sensing data is discussed.