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.

天文观测通常提供三维地图，编码观测通量在天球的两个角度和能量 / 频率上的分布。我们提出了一个深度学习框架，能够同时重建不同发射成分的光谱和点源群体的源计数分布，实现了从模拟地图中准确提取复杂形状的光谱和源计数分布的目标。