  The 21-cm emission from atomic hydrogen (HI) is one of the most important
tracers of the structure and dynamics of the interstellar medium. Thanks to
Galactic rotation, the line is Doppler shifted and, assuming a model for the
velocity field, data from gas line surveys can be deprojected along the line of
sight. However, given our vantage point in the Galaxy, such a reconstruction
suffers from a number of ambiguities. Here, we argue that those can be cured by
exploiting the spatial coherence of the gas density that is implied by the
physical processes shaping it. We have adopted a Bayesian inference framework
that allows reconstructing the three-dimensional map of HI and quantifying its
uncertainty. We employ data from the HI4PI compilation to produce
three-dimensional maps of Galactic HI. The reconstructed density shows
structure on a variety of scales. In particular, some spurs and spiral arms can
be identified with ease. We discuss the morphology of the surface mass density
and the radial and vertical profiles. The reconstructed three-dimensional HI
densities are available at https://doi.org/10.5281/zenodo.5956696.
