Scale-Adaptive filters for the detection/separation of compact sources
D. Herranz, J. L. Sanz, R. B. Barreiro, E. Martínez-gonzález · 2002
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).