An approach for the detection of point-sources in very high resolution microwave maps

This paper deals with the detection problem of extragalactic point-sources in multi-frequency, microwave sky maps that will be obtainable in future cosmic microwave background radiation (CMB) experiments with instruments capable of very high spatial resolution. With spatial resolutions that can be of order of 0.1-1.0 arcsec or better, the extragalactic point-sources will appear isolated. The same holds also for the compact structures due to the Sunyaev-Zeldovich (SZ) effect (both thermal and kinetic). This situation is different from the maps obtainable with instruments as WMAP or PLANCK where, because of the smaller spatial resolution (approximately 5-30 arcmin), the point-sources and the compact structures due to the SZ effect form a uniform noisy background (the "confusion noise"). Hence, the point-source detection techniques developed in the past are based on the assumption that all the emissions that contribute to the microwave background can be modeled with homogeneous and isotropic (often Gaussian) random fields and make use of the corresponding spatial power-spectra. In the case of very high resolution observations such an assumption cannot be adopted since it still holds only for the CMB. Here, we propose an approach based on the assumption that the diffuse emissions that contribute to the microwave background can be locally approximated by two-dimensional low order polynomials. In particular, two sets of numerical techniques are presented containing two different algorithms each. The performance of the algorithms is tested with numerical experiments that mimic the physical scenario expected for high Galactic latitude observations with the Atacama Large Millimeter/Submillimeter Array (ALMA).