Equiangular fan-beam computerized tomography reconstruction for a noncircular scanning locus

A derivative-free, two-dimensional equiangular fan-beam reconstruction formula for a noncircular scanning locus is derived under three practical conditions. The formula contains the same terms as the traditional formula, except that the constant source-to-origin distance is replaced by the source-to-origin distance as a function of the rotation angle. The correctness of this formula is tested in numerical simulation. The potential applications of the formula include fourth-generation CT, electron-beam Ct, SPECT, and x-ray microtomography.