The Wide-Field Imaging Interferometry Testbed (WIIT) is a wide-field spectral imaging Michelson interferometer developed at the NASA/Goddard Space Flight Center. WIIT is operational and effectively demonstrates imaging and spectroscopy over fields-of-view larger than the narrow primary beam footprint of a conventional Michelson interferometer. At the heart of this technique is the "double-Fourier" approach whereby the apertures and a delay line are both moved to collect interferograms over a 2D wide field detector grid simultaneously; one interferogram per detector pixel. This aggregate set of interferograms, as a function of baseline and delay line, is algorithmically processed to construct a single spatial-spectral cube with angular resolution approaching the ratio of the wavelength to the longest baseline. Herein we develop the mathematical spatial-spectral imaging model and the baseline processing algorithm and show results using simulated data and using WIIT testbed data.