A variational Bayesian approach for unsupervised super-resolution using mixture models of point and smooth sources applied to astrophysical map-making

Abstract

We present, in this paper, a new unsupervised method for joint image super-resolution and separation between smooth and point sources. For this purpose, we propose a Bayesian approach with a Markovian model for the smooth part and Student’s t-distribution for point sources. All model and noise parameters are considered unknown and should be estimated jointly with images. However, joint estimators (joint MAP or posterior mean) are intractable and an approximation is needed. Therefore, a new gradient-like variational Bayesian method is applied to approximate the true posterior by a free-form separable distribution. A parametric form is obtained by approximating marginals but with form parameters that are mutually dependent. Their optimal values are achieved by iterating them till convergence. The method was tested by the model-generated data and a real dataset from the Herschel space observatory.