Four-dimensional tomography based on a level set method
S Siltanen (University of Helsinki, Finland)

A novel time-dependent tomographic imaging modality with multiple source-detector pairs in fixed positions is discussed. All detectors record simultaneously time-dependent radiographic data ("X-ray videos") of a moving object, such as running engine, a mouse, or a beating human heart. The dynamic three-dimensional structure is reconstructed from projection data using a new computational method. Time is considered as an additional dimension in the problem, and a generalized level set method [Kolehmainen, Lassas, Siltanen, SIAM J Scientific Computation 30 (2008)] is applied in space-time. In this approach, the X-ray attenuation coefficient is modeled by the continuous level set function itself (instead of a constant) inside the domain defined by the level set, and by zero outside. Numerical examples with both simulated and measured data suggest that the method successfully regularizes the inverse problem by enforcing continuity both spatially and temporally.