Astronomical image restoration using variational methods and model combination

In this work we develop a variational framework for the combination of several prior models in Bayesian image restoration and apply it to astronomical images. Since each combination of a given observation model and a prior model produces a different posterior distribution of the underlying image, the use of variational posterior distribution approximation on each posterior will produce as many posterior approximations as priors we want to combine. A unique approximation is obtained here by finding the distribution on the unknown image given the observations that minimizes a linear convex combination of the Kullback–Leibler divergences associated with each posterior distribution. We find this distribution in closed form and also relate the proposed approach to other prior combination methods in the literature. Experimental results on both synthetic images and on real astronomical images validate the proposed approach.