Background-Source Separation in astronomical images with Bayesian probability theory (I): the method

A probabilistic technique for the joint estimation of background and sources with the aim of detecting faint and extended celestial objects is described. Bayesian probability theory is applied to gain insight into the coexistence of background and sources through a probabilistic two-component mixture model, which provides consistent uncertainties of background and sources. A multi-resolution analysis is used for revealing faint and extended objects in the frame of the Bayesian mixture model. All the revealed sources are parameterized automatically providing source position, net counts, morphological parameters and their errors.