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

Bayesian ICA-based source separation of Cosmic Microwave Background by a discrete functional approximation