Tracking Signal Subspace Invariance for Blind Separation and Classification of Nonorthogonal Sources in Correlated Noise
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Research Article Tracking Signal Subspace Invariance for Blind Separation and Classification of Nonorthogonal Sources in Correlated Noise Karim G. Oweiss1 and David J. Anderson2 1 Electrical 2 Electrical
& Computer Engineering Department, Michigan State University, East Lansing, MI 48824-1226, USA Engineering & Computer Science Department, University of Michigan, Ann Arbor, MI 48109-2122, USA
Received 1 October 2005; Revised 11 April 2006; Accepted 27 May 2006 Recommended by George Moustakides 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. Copyright © 2007 K. G. Oweiss and D. J. Anderson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
Multichannel signal processing aims at fusing data collected at several sensors in order to carry out an estimation task of signal sources. Generally speaking, the parameters to be estimated reveal important information characterizing the sources from which the data is observed. The aim of array signal processing is to extract these parameters with the minimal degree of uncertainty to enable detection and classification of these sources to take place. Many array signal processing algorithms rely on eigenstructure subspace methods performed either in the time domain, in the frequency domain, or in the composite time-frequency domain [1–3]. Regardless of which domain is used, eigenstructure based algorithms offer an
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