The detection of compact sources embedded in a background is a very common problem in many fields of Astronomy. In these lecture notes we present a review of different techniques developed for the detection and extraction of compact sources, with a especial focus on their application to the field of the cosmic microwave background radiation. In particular, we will consider the detection of extragalactic point sources and the thermal and kinematic Sunyaev-Zeldovich effects from clusters of galaxies.
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