Estimation of small motion for dynamic X-ray computed tomography using a general motion model and moments of projections

We propose a method for estimation of general (non-rigid) small motion for dynamic computed tomography (CT). In the proposed method we estimate motion parameters of the general motion model from the moments of the dynamic projections, inspired by the Helgason-Ludwig consistency conditions. The non-linear problem of solving a system involving composition of functions is dealt with in the Fourier transform space where it simplifies into a problem involving multiplicatively separable functions. The system is then linearized to solve for object motion. Numerical simulation results are shown for the proposed method for fan-beam geometry. The numerical simulation results show good agreement between estimated and true motion. The proposed method is X-ray dose efficient and does not need other aids such as gating or fiducidal markers.