Dynamic multi-source X-ray tomography using a spacetime level set method

A novel variant of the level set method is introduced for dynamic two-dimensional X-ray tomography. The target is allowed to change in time while being imaged by one or several source-detector pairs at a relatively high frame-rate. The algorithmic approach is motivated by the results in [Kolehmainen et al., SIAM J. Sci. Comput. 30(3)], showing that the modified level set method can tolerate highly incomplete projection data in stationary tomography. Furthermore, defining the level set function in spacetime enforces temporal continuity in the dynamic tomography context considered here. The reconstruction method is based on minimizing a nonlinear functional; the existence and uniqueness of a minimizer of the functional is proved under certain assumptions on the signal-to-noise ratio and the size of the regularization parameter. Numerical examples with both simulated and real X-ray data are included. The proposed method yields significantly better reconstruction quality than classical methods such as filtered back-projection and Tikhonov regularization. Furthermore, the methodology can be adapted to a wide range of measurement arrangements with one or more X-ray sources.