  We present an approach that combines photon spectrum correlation analysis
with the reconstruction of three-dimensional momentum distribution from
velocity map images in an efficient, single-step procedure. We demonstrate its
efficacy with the results from the photoionization of the $2p$-shell of argon
using the FLASH free-electron laser~(FEL). Distinct spectral features due to
the spin-orbit splitting of Ar$^+(2p^{-1})$ are resolved, despite the large
average bandwidth of the ionizing pulses from the FEL. This demonstrates a
clear advantage over the conventional analysis method, and it will be broadly
beneficial for velocity map imaging experiments with FEL sources. The retrieved
linewidth of the binding energy spectrum approaches the resolution limitation
prescribed by the spectrometers used to collect the data. Our approach presents
a path to extend spectral-domain ghost imaging to the case where the
photoproduct observable is high-dimensional.
