We present two new source extraction methods, based on Bayesian model selection and using the Bayesian Information Criterion (BIC). The first is a source detection filter, able to simultaneously detect point sources and estimate the image background. The second is an advanced photometry technique, which measures the flux, position (to sub-pixel accuracy), local background and point spread function. We apply the source detection filter to simulated Herschel-SPIRE data and show the filter's ability to both detect point sources and also simultaneously estimate the image background. We use the photometry method to analyse 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 characterises the nature of the source (distinguishing between a point source and extended source). We demonstrate the effect of including additional prior knowledge. Prior knowledge of the point spread function increase the precision of the flux measurement, while prior knowledge of the background has onlya 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 waveband) 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 FIS far-infrared all-sky survey. They are also implemented in a stand-alone, beta-version public tool that can be obtained at http://astronomy.sussex.ac.uk/$\sim$rss23/sourceMiner\_v0.1.2.0.tar.gz

Accepted for publication by ApJ (this version compiled used emulateapj.cls)