Blind source separation of positive and partially correlated data

Authors:
Wady Naanaa;Jean-Marc Nuzillard
Affiliations:
SOIE, Faculty of Sciences, Monastir, Tunisia;FRE CNRS, University of Reims, Reims Cedex, France
Venue:
Signal Processing
Year:
2005

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Abstract

Blind source separation (BSS) consists of processing a set of observed mixed signals to separate them into a set of unobservable original components. Various approaches have been employed to solve BSS problems using the strong assumption focusing on mutually uncorrelated (or orthogonal) source signals. However, in many real-life problems, signal orthogonality is not guaranteed.This paper introduces a new approach to BSS that can be applied to nonorthogonal signals. The orthogonality requirement is replaced by a partial orthogonality and a nonnegativity constraint which are well-suited for many real-world signals. An algebraic property is then exploited to express BSS problems in terms of constrained optimization. An efficient algorithm implementing the approach is reported and applied to examples from nuclear magnetic resonance spectroscopy.