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ABSTRACT  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 co‐existence of background and sources through a probabilistic two‐component mixture model, which provides consistent uncertainties of background and sources. A multiresolution analysis is used for revealing faint and extended objects in the frame of the Bayesian mixture model. All the revealed sources are parametrized automatically providing source position, net counts, morphological parameters and their errors.  We demonstrate the capability of our method by applying it to three simulated data sets characterized by different background and source intensities. The results of employing two different prior knowledge on the source signal distribution are shown. The probabilistic method allows for the detection of bright and faint sources independently of their morphology and the kind of background. The results from our analysis of the three simulated data sets are compared with other source detection methods. Additionally, the technique is applied to  ROSAT  All‐Sky Survey data.

Background–source separation in astronomical images with Bayesian probability theory – I. The method