Blind Separation of Noisy Multivariate Data Using Second-Order Statistics: Remote-Sensing Applications

In this paper a second-order method for blind source separation of noisy instantaneous linear mixtures is presented for the case where the signal order k is unknown. Its performance advantages are illustrated by simulations and by application to Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) multichannel visible/infrared data. The model assumes that m mixtures x of dimension n are observed, where x = Ap + Gw , and the underlying signal vector p has k A is the mixing matrix, G is diagonal, and w is a normalized white-noise vector. The algorithm estimates the Second-Order separation matrix A , signal Order k , and Noise and is therefore designated as SOON. SOON first iteratively estimates k and G using a scree metric, singular-value decomposition, and the expectation-maximization algorithm, and then determines the values of AP and W . The final step estimates A and the set of m signal vectors p using a variant of the joint-diagonalization method used in the Second-Order Blind Identification (SOBI) and Second-Order NonStationary (SONS) source-separation algorithms. The SOON extension of SOBI and SONS significantly improves their separation of simulated sources hidden in noise. SOON also reveals interesting thermal dynamics within AVIRIS multichannel visible/infrared imaging data not found by noise-adjusted principal-component analysis.