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/rc) ] −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 ≥ 0, q ≡ |~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). Subject headings: methods: analytical — methods: data analysis — techniques: image processing