Introducing constrained matched filters for improved separation of point sources from galaxy clusters

Matched filters (MFs) are elegant and widely used tools to detect and measure signals that resemble a known template in noisy data. However, they can perform poorly in the presence of contaminating sources of similar or smaller spatial scale than the desired signal, especially if signal and contaminants are spatially correlated. We introduce new multicomponent MF and matched multifilter (MMF) techniques that allow for optimal reduction of the contamination introduced by sources that can be approximated by templates. The application of these new filters is demonstrated by applying them to microwave and X-ray mock data of galaxy clusters with the aim of reducing contamination by point-like sources, which are well approximated by the instrument beam. Using microwave mock data, we show that our method allows for unbiased photometry of clusters with a central point source but requires sufficient spatial resolution to reach a competitive noise level after filtering. A comparison of various MF and MMF techniques is given by applying them to Planck multifrequency data of the Perseus galaxy cluster, whose brightest cluster galaxy hosts a powerful radio source known as Perseus A. We also give a brief outline how the constrained MF (CMF) introduced in this work can be used to reduce the number of point sources misidentified as clusters in X-ray surveys like the upcoming eROSITA all-sky survey. A python implementation of the filters is provided by the authors of this manuscript at \url{https://github.com/j-erler/pymf}.