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

Abstract

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. $\tau (x)={[1+{(x/r_c)}^2]}^{-\lambda },\lambda \ge 1/2,x\equiv |\vec{x}|$, and a background modeled by a homogeneous and isotropic random field, characterized by a power spectrum $P(q)\propto q^{-\gamma },\gamma \ge 0,q\equiv |\vec{q}|$. 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).

41 pages, 7 figures, submitted to ApJ

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