Cone-beam iterative reconstruction of a segment of a long object

This study was performed to investigate the iterative reconstruction of a segment of a long object using cone-beam projections acquired with a practical-sized detector. This reconstruction problem is commonly called the cone-beam long object problem. The cone-beam focal-point trajectories studied were either helical or helical with planar arcs. We assume that the long object is confined in a tall supporting cylinder and that the cone-beam detector is wide enough that the projections are not truncated transversely. If the detector is not wide enough, we use two asymmetric cone-beam detectors, each covering at least one-half of the field of view in the transverse direction. The detector size in the axial direction is not large enough to cover the segment. The detector size is used to determine the maximal helical pitch. A data sufficiency condition is established to design a focal-point trajectory. The trajectory then defines a convex hull. Projection rays that touch the region outside the convex hull and inside the supporting cylinder are discarded in the iterative algorithm. Computer simulations and experimental data verify that the proposed data acquisition and discarding strategy result in accurate segment reconstruction.