On Optimal selection of correlation matrices for matrix-pencil-based separation

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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.

Original languageEnglish
Pages (from-to)187-194
Number of pages8
JournalLecture Notes in Computer Science
Volume5441
DOIs
StatePublished - 2009
Event8th International Conference on Independent Component Analysis and Signal Separation, ICA 2009 - Paraty, Brazil
Duration: 15 Mar 200918 Mar 2009

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