A well-conditioned estimator for large-dimensional covariance matrices
Journal of Multivariate Analysis
On Optimal Selection of Correlation Matrices for Matrix-Pencil-Based Separation
ICA '09 Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation
Fast approximate joint diagonalization incorporating weight matrices
IEEE Transactions on Signal Processing
Blind separation of cyclostationary sources using joint block approximate diagonalization
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Shrinkage algorithms for MMSE covariance estimation
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
A blind source separation technique using second-order statistics
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
Asymptotic theory of mixed time averages and kth-order cyclic-moment and cumulant statistics
IEEE Transactions on Information Theory
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Maximum Likelihood (ML) blind separation of Gaussian sources with different temporal covariance structures generally requires the estimation of the underlying temporal covariance matrices. The possible availability of multiple realizations (''snapshots'') of the mixtures (all synchronized to some external stimulus) may enable such estimation. In general, however, since these temporal covariance matrices are high-dimensional, reliable estimation thereof might require a prohibitively large number of snapshots. In this work, we propose to take an alternative, partial and approximate ML approach, which regards a selected set of spatial sample-generalized-correlations of the observations (rather than the observations themselves) as the ''front-end'' data for the ML estimate. As we show, the implied Correlations-Based approximate ML (CBML) estimate, which can also be regarded as a weighted joint diagonalization approach, requires the estimation of considerably smaller covariance matrices, and can therefore be preferable to the ''full'' Data-Based ML (DBML) estimate. Therefore, although asymptotically sub-optimal, under sub-asymptotic conditions CBML can outperform the asymptotically optimal DBML, as we demonstrate in simulation.