Quantification of Tomographic Incompleteness in Cone-Beam Reconstruction

For situations of cone-beam (CB) scanning where the measurements are incomplete, we propose a method to quantify the severity of the missing information at each voxel. This incompleteness metric is geometric; it uses only the relative locations of all CB vertices with respect to the voxel in question, and does not apply global information, such as the object extent or the pattern of incompleteness of other voxels. The values are non-negative, with zero indicating “least incompleteness,” i.e., minimal danger of incompleteness artifacts. The incompleteness value can be related to the severity of the potential reconstruction artifact at the voxel location, independent of reconstruction algorithm. We performed a computer simulation of X-ray sources along a circular trajectory, and used small multidisk test-objects to examine the local effects of data incompleteness. The observed behavior of the reconstructed test-objects quantitatively matched the precalculated incompleteness values. A second simulation of a hypothetical SPECT breast imaging system used only 12 pinholes. Reconstructions were performed using analytic and iterative methods, and five reconstructed test-objects matched the behavior predicted by the incompleteness model. The model is based on known sufficiency conditions for data incompleteness, and provides strong predictive guidance for what can go wrong with incomplete CB data.