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., τ(x) = [1 + (x/r c ) 2 ] -λ , λ ≥ 1/2, x ≡ |x|, and a background modeled by a homogeneous and isotropic random field, characterized by a power spectrum P(q) ∝ q -γ , γ ≥ 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).