title: Theory and algorithms for image reconstruction on chords and within regions of interest.
abstract: We introduce a formula for image reconstruction on a chord of a general source trajectory. We subsequently develop three algorithms for exact image reconstruction on a chord from data acquired with the general trajectory. Interestingly, two of the developed algorithms can accommodate data containing transverse truncations. The widely used helical trajectory and other trajectories discussed in literature can be interpreted as special cases of the general trajectory, and the developed theory and algorithms are thus directly applicable to reconstructing images exactly from data acquired with these trajectories. For instance, chords on a helical trajectory are equivalent to the n-PI-line segments. In this situation, the proposed algorithms become the algorithms that we proposed previously for image reconstruction on PI-line segments. We have performed preliminary numerical studies, which include the study on image reconstruction on chords of two-circle trajectory, which is nonsmooth, and on n-PI lines of a helical trajectory, which is smooth. Quantitative results of these studies verify and demonstrate the proposed theory and algorithms.
authors.affiliation: University of Chicago, Department of Radiology, 5841 S. Maryland Avenue, Chicago, Illinois 60637, USA.
authors.forename: Yu
authors.initials: Y
authors.lastname: Zou
authors.forename: Xiaochuan
authors.initials: X
authors.lastname: Pan
authors.forename: Emil Y
authors.initials: EY
authors.lastname: Sidky
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D001921:Brain / Q000000981:diagnostic imaging*; D006801:Humans; D019047:Phantoms, Imaging; D011856:Radiographic Image Enhancement / Q000295:instrumentation / Q000379:methods*; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000295:instrumentation / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D014057:Tomography, X-Ray Computed / Q000379:methods*