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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 2  p -shell of argon using the Free-electron LASer in Hamburg 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.