Multi-dimensional signal separation with Gaussian processes
Antoine Liutkus, Roland Badeau, Gaël Richard · 2011
Gaussian process (GP) models are widely used in machine learning to account for spatial or temporal relationships between multivariate random variables. In this paper, we propose a formulation of underdetermined source separation in multidimensional spaces as a problem involving GP regression. The advantage of the proposed approach is firstly to provide a flexible means to include a variety of prior information concerning the sources and secondly to lead to minimum mean squared error estimates. We show that if the additive GPs are supposed to be locally-stationary, computations can be done very efficiently in the frequency domain. These findings establish a deep connection between GP and nonnegative tensor factorizations with the Itakura-Saito distance and we show that when the signals are monodimensional, the resulting framework coincides with many popular methods that are based on nonnegative matrix factorization and time-frequency masking.