Geometrically constrained permutation-free source separation in an undercomplete speech unmixing scenario

Frequency domain blind source separation (BSS) problems are typically solved in each frequency bin independently and therefore require additional measures to resolve the resulting permutation problem. In this paper, a frequency domain methodology is presented based on a recently introduced extension of Independent Component Analysis (ICA) to multi-variate components which uses a multi-variate activation function to model dependencies between frequency bins and therefore inherently manages to align most of the permutations. Since the latter approach shows slow convergence behaviour and is prone to converging to local optima, additional geometric constraints are used here to force the BSS algorithm to separate sources with a consistent direction of arrival (DOA) over all frequencies into a minimum number of output channels. DOA information is obtained from a priori knowledge or from subband analysis of partially separated source signals. The methodology is illustrated in an undercomplete acoustic source separation scenario with 3 speakers and 4 microphones.