Estimation of Local Data-Insufficiency in Motion-Corrected Helical CT

Previously we have proposed a reconstruction algorithm which corrects for known rigid motion in helical CT. This paper describes a method to determine data-insufficiency of helical CT data affected by rigid object motion. We propose a local measure that quantifies the degree to which Tuy's completeness condition is violated in each voxel. This measure identifies regions for which artifact-free reconstruction is not assured. For every voxel, a local data-insufficiency measure is computed. We call the resulting image the Tuy map. Its values range from 0 to 1, where high values indicate data-insufficiency. As shown by classic theory, exact reconstruction is not possible, where the Tuy map contains high values. The predictions based on this Tuy map were verified with simulated helical-CT data, where the object moved during the scan and the motion was correctly taken into account during reconstruction. We also analyzed the reconstruction from an actual motion-corrected CT-scan of a moving phantom. For motion-free helical scans, the Tuy map was close to zero everywhere and the reconstructions were artifact-free. Rigid motion induces an effective source trajectory (with respect to a stationary patient) which, combined with axial or even transaxial truncation, can cause incomplete sampling. In simulations with severe motion or transaxial detector truncation, the Tuy map contained high values and the reconstructions suffered from artifacts. In the phantom scan, the combination of a high pitch and severe motion created artifacts which the Tuy map successfully indicated. In all cases, the Tuy map indicated all regions with incomplete sampling which were prone to reconstruction artifacts. However, we also contrived a special case, where exact reconstruction was not assured although the local Tuy condition was satisfied. The proposed method provides a useful measure of data-incompleteness, which can be used to verify the validity of motion-corrected helical CT scans. The method is general and could also be useful for other tomographic problems for which no exact data sufficiency measures are available.