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

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.