Quantification of local reconstruction accuracy for helical CT with motion correction

In previous work, we have demonstrated the feasibility of rigid motion correction for helical CT brain imaging, using an optical motion tracking system. To correct for motion during reconstruction, the object is considered stationary, while the inverse of the motion is applied to the CT system. As a result, the original helical CT trajectory is replaced with a new, irregular trajectory. We have observed that, depending on the motion and the CT scanning parameters, the irregular motion corrected trajectory may not provide sufficient data for tomographic reconstruction. The known completeness conditions, such as the Tuy condition, assume untruncated projections and therefore can not be applied to helical CT, where the projections are axially truncated. Other groups have developed methods to quantify the degree to which sampling completeness is satisfied locally in pinhole SPECT. Here we propose a related approach to quantify the local completeness of the irregular CT trajectory, by assessing to which degree the local Tuy condition is unsatisfied. In a simulation experiment, we compare this empirical local completeness measure to the local occurrence of artifacts. The results indicate if the Tuy value is relatively high in some region, the reconstruction is likely to suffer from artifacts in this region.