Abstract
This paper considers the detection of point sources in two-dimensional astronomical images. The detection scheme we propose is based on peak statistics. We discuss the example of the detection of far galaxies in cosmic microwave background experiments throughout the paper, although the method we present is totally general and can be used in many other fields of data analysis. We consider sources with a Gaussian profile--that is, a fair approximation of the profile of a point source convolved with the detector beam in microwave experiments--on a background modeled by a homogeneous and isotropic Gaussian random field characterized by a scale-free power spectrum. Point sources are enhanced with respect to the background by means of linear filters. After filtering, we identify local maxima and apply our detection scheme, a Neyman-Pearson detector that defines our region of acceptance based on the a priori pdf of the sources and the ratio of number densities. We study the different performances of some linear filters that have been used in this context in the literature: the Mexican hat wavelet, the matched filter, and the scale-adaptive filter. We consider as well an extension to two dimensions of the biparametric scale-adaptive filter (BSAF). The BSAF depends on two parameters which are determined by maximizing the number density of real detections while fixing the number density of spurious detections. For our detection criterion the BSAF outperforms the other filters in the interesting case of white noise.
Highlights
A very challenging aspect of data analysis in astronomy is the detection of pointlike sources embedded in one- and twodimensional images
In order to define the region of acceptance R∗ that gives the highest number density of detections n∗ for a given number density of spurious detections n∗b, we consider a Neyman-Pearson detector (NPD) using number densities instead of probabilities
This is the case we find in cosmic microwave background (CMB) experiments, where the profile of the point source is given by the instrumental beam that can be approximated by a Gaussian
Summary
A very challenging aspect of data analysis in astronomy is the detection of pointlike sources embedded in one- and twodimensional images. Since the typical angular size of the galaxies in the sky is a few arcseconds and the angular resolution of the microwave detectors is typically greater than a few arcminutes, galaxies appear as points to the detector, which is unable to resolve their inner structure They are usually referred to as extragalactic point sources (EPS) in the CMB jargon. The problem with EPS is that galaxies are a very heterogeneous bundle of objects, from the radio galaxies that emit most of their radiation in the low-frequency part of the electromagnetic spectrum to the dusty galaxies that emit mainly in the infrared (Toffolatti et al [9], Guiderdoni et al [10], Tucci et al [11]) This makes it impossible to consider all of them as a single foreground to be separated from the other by means of multiwavelength observations and statistical component separation techniques.
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