An inversion formula for the cone-beam transform for arbitrary source trajectories

We introduce a forward model for the cone-beam X-ray Computed Tomography projection data measured in native geometries as a Fourier Integral Operator and present a corresponding filtered-backprojection type inversion formula. Our model and inversion formula can accommodate arbitrary source trajectories, arbitrary detector plane orientation, detector surface geometries, and other system related parameters. When the model parameters are chosen such that the forward model is equivalent to the cone-beam transform with helical or circular source trajectory, the inversion formula leads to the well-known Feldkamp’s method with the one-dimensional filtering in the tangential direction. In the final version of the manuscript we will present validation of the inversion formula using the conebeam projection data generated using GE’s software package CatSim.