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. $\tau (x) = {[1 + {(x/r_c)}^2]}^{-\lambda}, \lambda \geq {1/2}, x\equiv |\vec{x}|$, and a background modeled by a homogeneous and isotropic random field, characterized by a power spectrum $P(q)\propto q^{-\gamma}, \gamma \geq 0, q\equiv |\vec{q}|$. We make an n-dimensional treatment but consider two interesting astrophysical applications related to clusters of galaxies (Sunyaev-Zel'dovich effect and X-ray emission).