Maximum-likelihood detection of sources among Poissonian noise

A maximum likelihood (ML) technique for detecting compact sources in images of the X-ray sky is examined. Such images, in the relatively low exposure regime accessible to present X-ray observatories, exhibit Poissonian noise at background flux levels. A variety of source detection methods are compared via Monte Carlo, and the ML detection method is shown to compare favourably with the optimized-linear-filter (OLF) method when applied to a single image. Where detection proceeds in parallel on several images made in different energy bands, the ML method is shown to have some practical advantages which make it superior to the OLF method. Some criticisms of ML are discussed. Finally, a practical method of estimating the sensitivity of ML detection is presented, and is shown to be also applicable to sliding-box source detection.