Source separation for multi-spectral image data with Gaussian mixture priors, with application to the cosmic microwave background

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 is quantified as a Gaussian mixture model with an unknown number of factors. Markov chain Monte Carlo 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 results are shown. The technique suggested is easily applicable to other source separation applications by modifying some of the priors. The computational challenges of this application are large. Multivariate prior mixture models, that incorporate spatial smoothness of sources and dependencies between them, considerably complicate implementation. In addition, Planck data consist of 9 images of order 107 pixels each. We explore various functional approximation approaches to computing marginal posterior distributions, and compare performance with the best MCMC algorithms that we have been able to implement.