Consistency conditions upon 3D CT data and the wave equation

Source trajectories and reconstruction algorithms for clinical volumetric computerized tomography (VCT) will require optimization for efficiency and image quality. VCT data is highly overdetermined, satisfying an ultrahyperbolic partial differential equation. Characteristic boundary value problems for the hyperbolic wave equation and ultrahyperbolic equation are compared, focusing in this paper on a mathematically instructive open-gantry VCT geometry. This example provides physical insight into consistency conditions upon VCT data, clearly showing which information about the object can and cannot be recovered from a set of measured projections. Furthermore, this example demonstrates that efficient numerical solvers for the ultrahyperbolic equation can provide tremendous flexibility in the choice of reconstruction algorithm.