Informed FastICA: Semi-Blind Minimum Variance Distortionless Beamformer

Non-Gaussianity-based Independent Vector Extraction leads to the famous one-unit FastICA/FastIVA algorithm when the likelihood function is optimized using an approximate Newton-Raphson algorithm under the orthogonality constraint. In this paper, we replace the constraint with the analytic form of the minimum variance distortionless beamformer (MVDR), by which a semi-blind variant of FastICA/FastIVA is obtained. The side information here is provided by a weighted covariance matrix replacing the noise covariance matrix, the estimation of which is a frequent goal of neural beamformers. The algorithm thus provides an intuitive connection between model-based blind extraction and learning-based extraction. The algorithm is tested in simulations and speaker ID-guided speaker extraction, showing fast convergence and promising performance.

Independent Vector Extraction Constrained on Manifold of Half-Length Filters

Independent Vector Analysis (IVA) is a popular extension of Independent Component Analysis (ICA) for joint separation of a set of instantaneous linear mixtures, with a direct application in frequency-domain speaker separation or extraction. The mixtures are parameterized by mixing matrices, one matrix per mixture. This means that the IVA mixing model does not account for any relationships between parameters across the mixtures/frequencies. The separation proceeds jointly only through the source model, where statistical dependencies of sources across the mixtures are taken into account. In this paper, we propose a mixing model for joint blind source extraction where the mixing model parameters are linked across the frequencies. This is achieved by constraining the set of feasible parameters to the manifold of half-length separating filters, which has a clear interpretation and application in frequency-domain speaker extraction.