Detection of point sources on two-dimensional images based on peaks

This article 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 assume 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