Tracking Signal Subspace Invariance for Blind Separation and Classification of Nonorthogonal Sources in Correlated Noise

We investigate a new approach for the problem of source separation in correlated multichannel signal and noise environments. The framework targets the specific case when nonstationary correlated signal sources contaminated by additive correlated noise impinge on an array of sensors. Existing techniques targeting this problem usually assume signal sources to be independent, and the contaminating noise to be spatially and temporally white, thus enabling orthogonal signal and noise subspaces to be separated using conventional eigendecomposition. In our context, we propose a solution to the problem when the sources are nonorthogonal, and the noise is correlated with an unknown temporal and spatial covariance. The approach is based on projecting the observations onto a nested set of multiresolution spaces prior to eigendecomposition. An inherent invariance property of the signal subspace is observed in a subset of the multiresolution spaces that depends on the degree of approximation expressed by the orthogonal basis. This feature, among others revealed by the algorithm, is eventually used to separate the signal sources in the context of “best basis” selection. The technique shows robustness to source nonstationarities as well as anisotropic properties of the unknown signal propagation medium under no constraints on the array design, and with minimal assumptions about the underlying signal and noise processes. We illustrate the high performance of the technique on simulated and experimental multichannel neurophysiological data measurements