Fully Bayesian source separation with application to the cosmic microwave background

Abstract

We address the problem of source separation in the presence of prior information. We develop a fully Bayesian source separation technique that assumes a very flexible model for the sources, namely the Gaussian mixture model with an unknown number of factors, and utilize Markov chain Monte Carlo techniques for model parameter estimation. 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 which assumes completely blind separation of the sources. We report results on realistic simulations of expected Planck maps and on WMAP 5th year results. The technique suggested is easily applicable to other source separation applications by modifying some of the priors. Index Terms—Bayesian source separation, cosmic microwave background (CMB) radiation, Gibbs sampling, Markov chain Monte Carlo, Planck satellite mission.