PCAT-DE: Reconstructing point-like and diffuse signals in astronomical images using spatial and spectral information

Observational data from astronomical imaging surveys contain information about a variety of source populations and environments, and its complexity will increase substantially as telescopes become more sensitive. Even for existing observations, measuring the correlations between point-like and diffuse emission can be crucial to correctly inferring the properties of any individual component. For this task information is typically lost, either because of conservative data cuts, aggressive filtering or incomplete treatment of contaminated data. We present the code PCAT-DE, an extension of probabilistic cataloging designed to simultaneously model point-like and diffuse signals. This work incorporates both explicit spatial templates and a set of non-parametric Fourier component templates into a forward model of astronomical images, reducing the number of processing steps applied to the observed data. Using synthetic Herschel-SPIRE multiband observations, we demonstrate that point source and diffuse emission can be reliably separated and measured. We present two applications of this model. For the first, we perform point source detection/photometry in the presence of galactic cirrus and demonstrate that cosmic infrared background (CIB) galaxy counts can be recovered in cases of significant contamination. In the second we show that the spatially extended thermal Sunyaev-Zel'dovich (tSZ) effect signal can be reliably measured even when it is subdominant to the point-like emission from individual galaxies.