Scale-adaptive filters for the detection/separation of compact sources

This paper presents scale-adaptive filters that optimize the detection/separation of compact sources on a background. We assume that the sources have a multiquadric profile, i.e., tau(x) = [1 + (x/r(c))(2)](-lambda); lambda greater than or equal to 1/2; x = \x\, and a background modeled by a homogeneous and isotropic random field, characterized by a power spectrum P(q) proportional to q(-gamma), gamma greater than or equal to 0, q = \q\. We make an n-dimensional treatment but consider two interesting astrophysical applications related to clusters of galaxies (Sunyaev-Zeldovich effect and X-ray emission).