ROHSA: Regularized Optimization for Hyper-Spectral Analysis -
  Application to phase separation of 21 cm data
  Extracting the multiphase structure of the neutral interstellar medium (ISM)
is key to understand the star formation in galaxies. The radiative condensation
of the diffuse warm neutral medium producing a thermally unstable lukewarm
medium and a dense cold medium is closely related to the initial step which
leads the HI-to-H2 transition and the formation of molecular clouds. Up to now
the mapping of these phases out of 21 cm emission hyper-spectral cubes has
remained elusive mostly due to the velocity blending of individual cold
structures present on a given line of sight.
  To address this problem, we developed a new Gaussian decomposition algorithm
named ROHSA (Regularized Optimization for Hyper-Spectral Analysis) based on a
multi-resolution process from coarse to fine grid. ROHSA uses a regularized
non-linear least-square criterion to take into account simultaneously the
spatial coherence of the emission and the multiphase nature of the gas. In
order to obtain a solution with spatially smooth parameters, the optimization
is performed on the whole data cube at once. The performances of ROHSA were
tested on a synthetic observation computed from numerical simulations of
thermally bi-stable turbulence. An application on a 21 cm observation of a high
Galactic latitude region from the GHIGLS survey is presented.
  The evaluation of ROHSA on synthetic 21 cm observations shows that it is able
to recover the multiphase nature of the HI and physically meaningful
information about the underlying three-dimensional fields (density, velocity
and temperature). The application on a real 21 cm observation of a high
Galactic latitude field produces a picture of the multiphase HI, with isolated,
filamentary and narrow structures and wider, diffuse and space filling
components. The test-case field used here contains significant
intermediate-velocity clouds that were well mapped out by the algorithm.
