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We explore novel methods of recovering the original spectral line profilesfrom data obtained by instruments that sample those profiles with an extendedor multipeaked spectral transmission profile. The techniques are tested on dataobtained at high spatial resolution from the Fast Imaging Solar Spectrograph(FISS) grating spectrograph at the Big Bear Solar Observatory and from theInterferometric Bidimensional Spectrometer (IBIS) instrument at the Dunn SolarTelescope. The method robustly deconvolves wide spectral transmission profilesfor fields of view sampling a variety of solar structures (granulation, plageand pores) with a photometrical precision of less than 1%. The results andfidelity of the method are tested on data from IBIS obtained using severaldifferent 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 40wavelength samples. This approach is applicable for deconvolving large amountsof data from instruments with wide spectral transmission profiles, such as theVisible Tunable Filter (VTF) on the DKI Solar Telescope (DKIST). We alsoinvestigate its application to future instruments by recovering spectral lineprofiles obtained with a theoretical multi-peaked spectral transmissionprofile.  We further discuss the limitations of this deconvolutional approach throughthe analysis of the dimensionality of the original and multiplexed data.

Spectral deconvolution with deep learning: removing the effects of spectral PSF broadening