Filter design for the detection of compact sources embedded in non-stationary noise plus a deterministic background

Detection of a compact signal with a given profile mixed with a deterministic background and non-stationary noise is an issue of great interest in many scientific areas. In this paper, we propose a methodology based on filter design, that allows both the removal of the background and the estimation of the signal amplitude. Under certain conditions this filter is a wavelet with several vanishing moments. In particular, we apply this technique to the detection and estimation of extragalactic point sources in microwave maps. We show with numerical simulations that the filter is very effective at source detection/estimation. We want to remark that this method can be also applied to the analysis of signals and images in other fields.