Gaussian processes for source separation

In this paper we present a probabilistic method for source separation in the case where each source has a certain unknown temporal structure. We tackle the problem of source separation by maximum pseudo-likelihood estimation, representing the latent function which characterizes the temporal structure of each source by a random process with a Gaussian prior. The resulting pseudo-likelihood of the data is Gaussian, determined by a mixing matrix as well as by the predictive mean and covariance matrix that can be easily computed by Gaussian process (GP) regression. Gradient-based optimization is applied to estimate the demixing matrix through maximizing the log-pseudo-likelihood of the data. Numerical experiments confirm the useful behavior of our method, compared to existing source separation methods.