Abstract
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.
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© 2009 Springer-Verlag Berlin Heidelberg
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Yeredor, A. (2009). On Optimal Selection of Correlation Matrices for Matrix-Pencil-Based Separation. In: Adali, T., Jutten, C., Romano, J.M.T., Barros, A.K. (eds) Independent Component Analysis and Signal Separation. ICA 2009. Lecture Notes in Computer Science, vol 5441. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00599-2_24
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DOI: https://doi.org/10.1007/978-3-642-00599-2_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00598-5
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