  We explore novel methods of recovering the original spectral line profiles
from data obtained by instruments that sample those profiles with an extended
or multipeaked spectral transmission profile. The techniques are tested on data
obtained at high spatial resolution from the Fast Imaging Solar Spectrograph
(FISS) grating spectrograph at the Big Bear Solar Observatory and from the
Interferometric Bidimensional Spectrometer (IBIS) instrument at the Dunn Solar
Telescope. The method robustly deconvolves wide spectral transmission profiles
for fields of view sampling a variety of solar structures (granulation, plage
and pores) with a photometrical precision of less than 1%. The results and
fidelity of the method are tested on data from IBIS obtained using several
different spectral resolution modes.
  The method, based on convolutional neural networks (CNN), is extremely fast,
performing about $10^5$ deconvolutions per second on a CPU and $10^6$
deconvolutions per second on NVIDIA TITAN RTX GPU for a spectrum with 40
wavelength samples. This approach is applicable for deconvolving large amounts
of data from instruments with wide spectral transmission profiles, such as the
Visible Tunable Filter (VTF) on the DKI Solar Telescope (DKIST). We also
investigate its application to future instruments by recovering spectral line
profiles obtained with a theoretical multi-peaked spectral transmission
profile.
  We further discuss the limitations of this deconvolutional approach through
the analysis of the dimensionality of the original and multiplexed data.
