A sparse approach to astronomical point source detection

In this work we introduce a method for the detection of point sources in images based on a l₁-norm sparse approximation. The method is inspired on astronomical image analysis but is directly applicable to any kind of images. We introduce a `top-to-bottom´ detection algorithm that can greatly reduce the computational burden of detection if the images are sufficiently well-behaved, in the sense that sources are truly sparse and the chances of source overlapping are small. We test our ideas with simulated faint sources embedded in white noise, comparing the results with the matched filter detector for a number of detection thresholds. We show that the sparse detection approach leads to better results in the ROC curve than the matched filter detector. Moreover, with the sparse approach it is possible to provide an objective stopping criterion for the detection algorithm.