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We review the well-known matched filter method for the detection of pointsources in astronomical images. This is shown to be optimal (that is, tosaturate the Cramer--Rao bound) under stated conditions that are very strong:an isolated source in background-dominated imaging with perfectly knownbackground level, point-spread function, and noise models. We show that thematched filter produces a maximum-likelihood estimate of the brightness of apurported point source, and this leads to a simple way to combine multipleimages---taken through the same bandpass filter but with different noise levelsand point-spread functions---to produce an optimal point source detection map.We then extend the approach to images taken through different bandpass filters,introducing the SED-matched filter, which allows us to combine images takenthrough different filters, but requires us to specify the colors of the objectswe wish to detect. We show that this approach is superior to some methodstraditionally employed, and that other traditional methods can be seen asinstances of SED-matched filtering with implied (and often unreasonable)priors. We present a Bayesian formulation, including a flux prior that leads toa closed-form expression with low computational cost.

Principled point-source detection in collections of astronomical images