Methods for analytic reconstruction for multi-source inverse geometry CT

Disclosed are embodiments of methods for reconstructing x-ray projection data (e.g., one or more sinograms) acquired using a multi-source, inverse-geometry computed tomography ("IGCT") scanner. One embodiment of a first method processes an IGCT sinogram by rebinning first in "z" and then in "xy," with feathering applied during the "xy" rebinning. This produces an equivalent of a multi-axial 3rd generation sinogram, which may be further processed using a parallel derivative and/or Hilbert transform. A TOM-window (with feathering) technique and a combined backprojection technique may also be applied to produce a reconstructed volume. An embodiment of a second method processes an IGCT sinogram using a parallel derivative and/or redundancy weighting. The second method may also use signum weighting, TOM-windowing (with feathering), backprojection, and a Hilbert Inversion to produce another reconstructed volume.