Bayesian methods of astronomical source extraction

We present two new source extraction methods, based on Bayesian model selection and using the Bayesian information criterion. The first is a source detection filter, which is able to simultaneously detect point sources and estimate the image background. The second is an advanced photometry technique that measures the flux, position ( to subpixel accuracy), local background, and point-spread function. We apply the source detection filter to simulated Herschel SPIRE data and demonstrate the filter's ability to both detect point sources and simultaneously estimate the image background. We use the photometry method to analyze a simple simulated image containing a source of unknown flux, position, and point-spread function; we not only accurately measure these parameters but also determine their uncertainties (using Markov chain Monte Carlo sampling). The method also characterizes the nature of the source (distinguishing between a point source and an extended source). We demonstrate the effect of including additional prior knowledge. Prior knowledge of the point- spread function increases the precision of the flux measurement, while prior knowledge of the background has only a small impact. In the presence of higher noise levels, we show that prior positional knowledge (such as might arise from a strong detection in another wave band) allows us to accurately measure the source flux even when the source is too faint to be detected directly. These methods are incorporated in SUSSEXtractor, the source extraction pipeline for the forthcoming Akari Far-Infrared Surveyor all- sky survey. They are also implemented in a stand-alone, beta-version tool that is freely available.