Estimating the number of sources in a noisy convolutive mixture using BIC

The number of source signals in a noisy convolutive mixture is determined based on the exact log-likelihoods of the candidate models. In (Olsson and Hansen, 2004), a novel probabilistic blind source separator was introduced that is based solely on the time-varying second-order statistics of the sources. The algorithm, known as ‘KaBSS’, employs a Gaussian linear model for the mixture, i.e. AR models for the sources, linear mixing filters and a white Gaussian noise model. Using an EM algorithm, which invokes the Kalman smoother in the E-step, all model parameters are estimated and the exact posterior probability of the sources conditioned on the observations is obtained. The log-likelihood of the parameters is computed exactly in the process, which allows for model evidence comparison assisted by the BIC approximation. This is used to determine the activity pattern of two speakers in a convolutive mixture of speech signals.