One-step image reconstruction from incomplete data in computer tomography

The authors develop a projection operator that simultaneously projects onto the set of all functions satisfying raysum constraints in parallel-beam CT. The projector can be directly extended to the fan-beam case through the process of rebinning. The projector generates a solution that is closest to the initial estimate among all the functions that are consistent with the available raysum data. It realizes the ART (algebraic reconstruction technique) in one step. The projector furnishes the one-step projection reconstruction (OSPR) for any arbitrary configurations of missing data. Because the projection is one-step, there can be a significant reduction in the number of online computations and memory requirements, especially when the missing data exhibit some pattern within a view or between views.