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 such sources are described by a spherical (central) profile and that the background 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 Gaussian source profiles and scale-free power spectra to represent the background.