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., τ( x ) = [1 + ( x / r c ) 2 ] -λ ,λ ≥ , x ≡ | |, and a background modeled by a homogeneous and isotropic random field, characterized by a power spectrum P ( q ) ∝ q -γ ,γ ≥ 0, 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).