Estimation of the spatial information in Gaussian model based audio source separation using weighted spectral bases

In Gaussian model based audio source separation, source spatial images are modelled by Gaussian distributions. The covariance matrices of the distributions are represented by source variances and spatial covariance matrices. Accordingly, the likelihood of an observed mixture of independent source signals is parametrized by the variances and the covariance matrices. The separation is performed by estimating the parameters and applying multichannel Wiener filtering. Assuming that spectral basis matrices trained on source power spectra are available, this work proposes a method to estimate the parameters by maximizing the likelihood using Expectation-Maximization. In terms of normalization, the variances are estimated applying singular value decomposition. Furthermore, by building weighted matrices from vectors of the trained matrices, semi-supervised non-negative matrix factorization is applied to estimate the spatial covariance matrices. The experimental results prove the efficiency of the proposed algorithm in reverberant environments.