Scale‐adaptive Filters for the Detection/Separation of Compact Sources

This paper presents scale-adaptive filters that optimize thedetection/separation of compact sources on a background. We assume that thesources have a multiquadric profile, i. e. $\tau (x) = {[1 +{(x/r_c)}^2]}^{-\lambda}, \lambda \geq {1/2}, x\equiv |\vec{x}|$, and abackground modeled by a homogeneous and isotropic random field, characterizedby a power spectrum $P(q)\propto q^{-\gamma}, \gamma \geq 0, q\equiv|\vec{q}|$. We make an n-dimensional treatment but consider two interestingastrophysical applications related to clusters of galaxies (Sunyaev-Zel'dovicheffect and X-ray emission).Comment: 41 pages, 7 figures, submitted to Ap