Optimal detection of sources on a homogeneous and isotropic background

This paper introduces the use of pseudofilters that optimize the detection/ extraction of sources on a background. We assume as a first approach that s uch sources are described by a spherical (central) profile and that the bac kground is represented by a homogeneous and isotropic random field. We make an n-dimensional treatment, placing emphasis on astrophysical applications for spectra, images, and volumes, for the cases of exponential and Gaussia n source profiles and scale-free power spectra to represent the background.