Dependent Gaussian mixture models for source separation

Source separation is a common task in signal processing and is often analogous to factor analysis. In this work we look at a factor analysis model for source separation of multi-spectral image data where prior information about the sources and their dependencies is quantified as a multivariate Gaussian mixture model with an unknown number of factors. Variational Bayes techniques for model parameter estimation are used. The development of this methodology is motivated by the need to bring an efficient solution to the separation of components in the microwave radiation maps to be obtained by the satellite mission Planck which has the objective of uncovering cosmic microwave background radiation. The proposed algorithm successfully incorporates a rich variety of prior information available to us in this problem in contrast to most of the previous work that assumes completely blind separation of the sources. Results on realistic simulations of Planck maps and on WMAP 5th year images are shown. The technique suggested is easily applicable to other source separation applications by modifying some of the priors.