A deep learning framework for jointly extracting spectra and source-count distributions in astronomy

Astronomical observations typically provide three-dimensional maps, encoding the distribution of the observed flux in (1) the two angles of the celestial sphere and (2) energy/frequency. An important task regarding such maps is to statistically characterize populations of point sources too dim to be individually detected. As the properties of a single dim source will be poorly constrained, instead one commonly studies the population as a whole, inferring a source-count distribution (SCD) that describes the number density of sources as a function of their brightness. Statistical and machine learning methods for recovering SCDs exist; however, they typically entirely neglect spectral information associated with the energy distribution of the flux. We present a deep learning framework able to jointly reconstruct the spectra of different emission components and the SCD of point-source populations. In a proof-of-concept example, we show that our method accurately extracts even complex-shaped spectra and SCDs from simulated maps.