  A functional approximation to implement Bayesian source separation analysis
is introduced and applied to separation of the Cosmic Microwave Background
(CMB) using WMAP data. The approximation allows for tractable full-sky map
reconstructions at the scale of both WMAP and Planck data and models the
spatial smoothness of sources through a Gaussian Markov random field prior. It
is orders of magnitude faster than the usual MCMC approaches. The performance
and limitations of the approximation are also discussed.
