Stereo Source Separation and Source Counting with MAP Estimation with Dirichlet Prior Considering Spatial Aliasing Problem

In this paper, we propose a novel sparse source separation method that can estimate the number of sources and time-frequency masks simultaneously, even when the spatial aliasing problem exists. Recently, many sparse source separation approaches with time-frequency masks have been proposed. However, most of these approaches require information on the number of sources in advance. In our proposed method, we model the phase difference of arrival (PDOA) between microphones with a Gaussian mixture model (GMM) with a Dirichlet prior. Then we estimate the model parameters by using the maximum a posteriori (MAP) estimation based on the EM algorithm. In order to avoid one cluster being modeled by two or more Gaussians, we utilize a sparse distribution modeled by the Dirichlet distributions as the prior of the GMM mixture weight. Moreover, to handle wide microphone spacing cases where the spatial aliasing problem occurs, the indeterminacy of modulus 2πk in the phase is also included in our model. Experimental results show good performance of our proposed method.