A general scheme for velocity tomography

With the rapid development of x-ray source and detector technologies, multi-source scanners become a hot topic in the CT field, which can acquire several projections simultaneously. Aided with the ECG-gating technique, the multi-source scanner can collect sufficient projections to reconstruct one or more specific phases of a beating heart. Hence, we are motivated to develop velocity tomography as a new dynamic imaging mode to recover the velocity field from the projections. First, we derive a velocity field constraint equation subject to the mass conservation. Then, we present a two-step general scheme to estimate the velocity field. The first step directly or indirectly computes partial derivatives. The second step iteratively determines the velocity field subject to the constraint equation and other conditions. Finally, we describe numerical experiments in the fan-beam geometry to demonstrate the correctness and utility of our scheme.