Blind source separation via the second characteristic function
Signal Processing
Blind source separation via generalized eigenvalue decomposition
The Journal of Machine Learning Research
The generalized eigendecomposition approach to the blind source separation problem
Digital Signal Processing
A blind source separation technique using second-order statistics
IEEE Transactions on Signal Processing
Blind source-separation using second-order cyclostationarystatistics
IEEE Transactions on Signal Processing
Blind separation of instantaneous mixtures of nonstationary sources
IEEE Transactions on Signal Processing
Blind source separation based on time-frequency signalrepresentations
IEEE Transactions on Signal Processing
A new performance index for ICA: properties, computation and asymptotic analysis
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
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The Matrix-Pencil approach to blind source separation estimates the mixing matrix from the Generalized Eigenvalue Decomposition (GEVD), or Exact Joint Diagonalization, of two "target-matrices". In a Second-Order-Statistics framework, these target-matrices are two different correlation matrices (e.g., at different lags, taken over different time-intervals, etc.), attempting to capture the diversity of the sources (e.g., diverse spectra, different nonstationarity profiles, etc.). A central question in this context is how to best choose these target-matrices, given a statistical model for the sources. To answer this question, we consider a general paradigm for the target-matrices, viewed as two "generalized correlation" matrices, whose structure is governed by two selected "Association-Matrices". We then derive an explicit expression (assuming Gaussian sources) for the resulting Interference-to-Source Ratio (ISR) in terms of the Association-Matrices. Subsequently, we show how to minimize the ISR with respect to these matrices, leading to optimized selection of the matrix-pair for GEVD-based separation.