Matrix analysis
Jacobi Angles for Simultaneous Diagonalization
SIAM Journal on Matrix Analysis and Applications
Joint Approximate Diagonalization of Positive Definite Hermitian Matrices
SIAM Journal on Matrix Analysis and Applications
Second-order blind source separation in the Fourier space of data
Signal Processing
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
SPWHOS '97 Proceedings of the 1997 IEEE Signal Processing Workshop on Higher-Order Statistics (SPW-HOS '97)
The Journal of Machine Learning Research
Adaptive blind source separation by second order statistics and natural gradient
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 05
Generalized second order identifiability condition and relevant testing technique
ICASSP '00 Proceedings of the Acoustics, Speech, and Signal Processing, 2000. on IEEE International Conference - Volume 05
A blind source separation technique using second-order statistics
IEEE Transactions on Signal Processing
An instantaneous formulation of mixtures for blind separation of propagating waves
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Blind separation of mixture of independent sources through aquasi-maximum likelihood approach
IEEE Transactions on Signal Processing
Blind separation of instantaneous mixtures of nonstationary sources
IEEE Transactions on Signal Processing
Quadratic optimization for simultaneous matrix diagonalization
IEEE Transactions on Signal Processing
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This paper focuses on the blind separation of stationary colored sources using the second-order statistics (SOS) of their instantaneous mixtures. We first start 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 function 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. If that is not the case then, further treatments will be 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 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.