  The topology and dynamics of the solar chromosphere are greatly affected by
the presence of magnetic fields. The magnetic field can be inferred by
analyzing polarimetric observations of spectral lines. Polarimetric signals
induced by chromospheric magnetic fields are, however, particularly weak, and
in most cases very close to the detection limit of current instrumentation.
Because of this, there are only few observational studies that have
successfully reconstructed the three components of the magnetic field vector in
the chromosphere. Traditionally, the signal-to-noise ratio of observations has
been improved by performing time-averages or spatial averages, but in both
cases, some information is lost. More advanced techniques, like
principal-component-analysis, have also been employed to take advantage of the
sparsity of the observations in the spectral direction. In the present study,
we propose to use the spatial coherence of the observations to reduce the noise
using deep-learning techniques. We design a neural network that is capable of
recovering weak signals under a complex noise corruption (including
instrumental artifacts and non-linear post-processing). The training of the
network is carried out without a priori knowledge of the clean signals, or an
explicit statistical characterization of the noise or other corruption. We only
use the same observations as our generative model. The performance of this
method is demonstrated on both, synthetic experiments and real data. We show
examples of the improvement in typical signals obtained in current telescopes
such as the Swedish 1-meter Solar Telescope. The presented method can recover
weak signals equally well no matter on what spectral line or spectral sampling
is used. It is especially suitable for cases when the wavelength sampling is
scarce.
