  We review the well-known matched filter method for the detection of point
sources in astronomical images. This is shown to be optimal (that is, to
saturate the Cramer--Rao bound) under stated conditions that are very strong:
an isolated source in background-dominated imaging with perfectly known
background level, point-spread function, and noise models. We show that the
matched filter produces a maximum-likelihood estimate of the brightness of a
purported point source, and this leads to a simple way to combine multiple
images---taken through the same bandpass filter but with different noise levels
and 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 taken
through different filters, but requires us to specify the colors of the objects
we wish to detect. We show that this approach is superior to some methods
traditionally employed, and that other traditional methods can be seen as
instances of SED-matched filtering with implied (and often unreasonable)
priors. We present a Bayesian formulation, including a flux prior that leads to
a closed-form expression with low computational cost.
