The next generation of radio telescopes will generate exabytes of data on hundreds of millions of objects, making automated methods for the detection of astronomical objects ("sources") essential. Of particular importance are faint, diffuse objects embedded in noise. There is a pressing need for source finding software that identifies these sources, involves little manual tuning, yet is tractable to calculate. We first give a novel image discretisation method that incorporates uncertainty about how an image should be discretised. We then propose a hierarchical prior for astronomical images, which leads to a Bayes factor indicating how well a given region conforms to a model of source that is exceptionally unconstrained, compared to a model of background. This enables the efficient localisation of regions that are "suspiciously different" from the background distribution, so our method looks not for brightness but for anomalous distributions of intensity, which is much more general. The model of background...
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