Principled Point-source Detection in Collections of Astronomical Images

Abstract There is almost no data analysis operation more important to astronomy than the detection of sources (stars or galaxies, say) in imaging. Here we write down a set of reasonable assumptions for well-understood (or well-calibrated) background-dominated imaging (faint sources) and find the detection methods that flow from those assumptions. Our methods are hypothesis comparisons, involving matched filters. We show that they are generally preferable to one-hypothesis ( p -value or n -sigma-deviation) methods, especially for avoiding spurious detection of nonstar image features. We consider the case in which there are multiple images at each point on the sky, and—more importantly for our purposes—when those images are taken through different bandpasses. Detection in multiband imaging involves making choices about the range of colors or spectral energy distributions to which the method will be most sensitive; we deliver methods based on Bayesian decision theory and also frequentist methods that deliver similar outcomes in real-data tests. We discuss relationships between these methods and standard practices. The methods we present perform well, but our main point is that methods should be principled—that is, they should flow from our fundamental assumptions about the data.