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Independent Vector Analysis via Log-Quadratically Penalized Quadratic Minimization

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Document pages: 11 pages

Abstract: We propose a new algorithm for blind source separation of convolutivemixtures using independent vector analysis. This is an improvement over thepopular auxiliary function based independent vector analysis (AuxIVA) withiterative projection (IP) or iterative source steering (ISS). We introduceiterative projection with adjustment (IPA), whereas we update one demixingfilter and jointly adjust all the other sources along its current direction. Weimplement this scheme as multiplicative updates by a rank-2 perturbation of theidentity matrix. Each update involves solving a non-convex minimization problemthat we term log-quadratically penalized quadratic minimization (LQPQM), thatwe think is of interest beyond this work. We find that the global minimum of anLQPQM can be efficiently computed. In the general case, we show that all itsstationary points can be characterized as zeros of a kind of secular equation,reminiscent of modified eigenvalue problems. We further prove that the globalminimum corresponds to the largest of these zeros. We propose a simpleprocedure based on Newton-Raphson seeded with a good initial point toefficiently compute it. We validate the performance of the proposed method forblind acoustic source separation via numerical experiments with reverberantspeech mixtures. We show that not only is the convergence speed faster in termsof iterations, but each update is also computationally cheaper. Notably, forfour and five sources, AuxIVA with IPA converges more than twice as fast ascompeting methods.

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