title: A unified analysis of FBP-based algorithms in helical cone-beam and circular cone- and fan-beam scans.
abstract: A circular scanning trajectory is and will likely remain a popular choice of trajectory in computed tomography (CT) imaging because it is easy to implement and control. Filtered-backprojection (FBP)-based algorithms have been developed previously for approximate and exact reconstruction of the entire image or a region of interest within the image in circular cone-beam and fan-beam cases. Recently, we have developed a 3D FBP-based algorithm for image reconstruction on PI-line segments in a helical cone-beam scan. In this work, we demonstrated that the 3D FBP-based algorithm indeed provided a rather general formulation for image reconstruction from divergent projections (such as cone-beam and fan-beam projections). On the basis of this formulation we derived new approximate or exact algorithms for image reconstruction in circular cone-beam or fan-beam scans, which can be interpreted as special cases of the helical scan. Existing algorithms corresponding to the derived algorithms were identified. We also performed a preliminary numerical study to verify our theoretical results in each of the cases. The results in the work can readily be generalized to other non-circular trajectories.
authors.affiliation: Department of Radiology, The University of Chicago, 5841 S Maryland Avenue, Chicago, IL 60637, USA.
authors.forename: Xiaochuan
authors.initials: X
authors.lastname: Pan
authors.forename: Dan
authors.initials: D
authors.lastname: Xia
authors.forename: Yu
authors.initials: Y
authors.lastname: Zou
authors.forename: Lifeng
authors.initials: L
authors.lastname: Yu
mesh_terms: D000465:Algorithms; D021621:Imaging, Three-Dimensional / Q000379:methods*; D019047:Phantoms, Imaging; D011856:Radiographic Image Enhancement / Q000379:methods*; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D036542:Tomography, Spiral Computed / Q000295:instrumentation / Q000379:methods*