A general framework for second order blind separation of stationary colored sources
Résumé
This paper focuses on the blind separation of stationary colored sources using the second order statistics of their instantaneous mixtures. We start first by presenting a brief overview of existing contributions in that field. Then, we present, necessary and sufficient conditions for the identifiability and partial identifiability using a finite set of correlation matrices. These conditions depend on the autocorrelation fonction of the unknown sources. However, it is shown here that they can be tested directly from the observation through the decorrelator output. This issue is of prime importance to decide whether the sources have been well separated or else if further treatments are needed. We then propose an identifiability testing based on resampling (jackknife) technique, that is validated by simulation results. Secondly, we present an iterative blind source separation method using second order statistics (SOS) and natural gradient technique. This algorithm has a number of attractive properties including its simplicity and 'easy' generalization to adaptive or convolutive schemes. Asymptotic performance analysis of this method is performed. Several numerical simulations are presented, to assess the theoretical results w.r.t the 'separability' testing, to demonstrate the effectiveness of the gradient-type decorrelation method and to validate the theoretical expression of the asymptotic performance index.
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