Neutron direct-geometry time-of-flight chopper spectroscopy is instrumental in studying fundamental excitations of vibrational and/or magnetic origin. We report here that techniques in super-resolution optical imagery (which is in real-space) can be adapted to enhance resolution and reduce noise for a neutron spectroscopy (an instrument for mapping excitations in reciprocal space). The procedure to reconstruct super-resolution energy spectra of phonon density of states relies on a realization of multiframe registration, accurate determination of the energy-dependent point spread function, asymmetric nature of instrument resolution broadening, and iterative reconstructions. Applying these methods to phonon density of states data for a graphite sample demonstrates contrast enhancement, noise reduction, and ∼5-fold improvement over nominal energy resolution. The data were collected at three different incident energies measured at the wide angular-range chopper spectrometer at the Spallation Neutron Source.