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An acoustically-motivated spatial prior for under-determined reverberant source separation

We consider the task of under-determined reverberant audio source separation. We model the contribution of each source to all mixture channels in the time-frequency domain as a zero-mean Gaussian random vector with full-rank spatial covariance matrix. We introduce an inverse Wishart prior over the covariance matrices, whose mean is given by the theory of statistical room acoustics and whose variance is learned from training data. We then derive an Expectation-Maximization (EM) algorithm to estimate the model parameters in the Maximum A Posteriori (MAP) sense given prior knowledge about the microphone spacing and the source positions. This algorithm provides a principled solution to the well-known permutation problem and achieves better separation performance than other algorithms exploiting the same prior knowledge.