Joint Bayesian separation and restoration of cosmic microwave background from convolutional mixtures

We propose a Bayesian approach to joint source separation and restoration for astrophysical diffuse sources. We constitute a prior statistical model for the source images by using their gradient maps.We assume a t-distribution for the gradient maps in different directions, because it is able to fit both smooth and sparse data. A Monte Carlo technique, called Langevin sampler, is used to estimate the source images and all the model parameters are estimated by using deterministic techniques.