title: The rotate-plus-shift C-arm trajectory. Part II. Exact reconstruction from less than 180° rotation.
abstract: OBJECTIVE
  CT reconstruction requires an angular coverage of 180° or more for each point within the field of measurement. Thus, common trajectories use a 180° plus fan angle rotation. This is sometimes combined with a translation of the rotational isocenter in order to achieve circular trajectories with an isocenter different from the mechanical rotation center or elliptical trajectories. Rays measured redundantly are appropriately weighted. In case of an angular coverage smaller than 180°, the reconstructed images suffer from limited angle artifacts. In mechanical constructions with a rotation range limited to less than 180° plus fan angle, the angular coverage can be extended by adding one or two shifts to the rotational motion. If the missing angle is less than the fan angle, the shifts can completely compensate for the limited rotational capabilities.
  
  
  METHODS
  The authors give weight functions that can be viewed as generalized Parker weights, which can be applied to the raw data before image reconstruction. Raw data of Forbild phantoms using the rotate-plus-shift trajectory are simulated with the geometry of a typical mobile flat detector-based C-arm system. Filtered backprojection (FBP) reconstructions using the new redundancy weight are performed and compared to FBP reconstructions of limited angle scans as well as short-scan reference trajectories using Parker weight.
  
  
  RESULTS
  The new weighting method is exact in 2D, and for 3D Feldkamp-type reconstructions, it is exact in the mid-plane. The proposed weight shows a mathematically exact match with Parker weight for conventional short-scan trajectories. Reconstructions of rotate-plus-shift trajectories using the new weight do not suffer from limited angle artifacts, whereas scans limited to less than 180° without shift show prominent artifacts. Image noise in rotate-plus-shift scans is comparable to that of corresponding short scans.
  
  
  CONCLUSIONS
  The new weight function enables the straightforward reconstruction using filtered backprojection of data acquired with the rotate-plus-shift C-arm trajectory and a large variety of other advanced trajectories.
authors.affiliation: Medical Physics in Radiology, German Cancer Research Center (DKFZ), Im Neuenheimer Feld 280, Heidelberg 69120, Germany.
authors.forename: Jan
authors.initials: J
authors.lastname: Kuntz
authors.affiliation: Ziehm Imaging GmbH, Donaustraße 31, Nürnberg 90451, Germany.
authors.forename: Ludwig
authors.initials: L
authors.lastname: Ritschl
authors.affiliation: Medical Physics in Radiology, German Cancer Research Center (DKFZ), Im Neuenheimer Feld 280, Heidelberg 69120, Germany.
authors.forename: Michael
authors.initials: M
authors.lastname: Knaup
authors.affiliation: Medical Physics in Radiology, German Cancer Research Center (DKFZ), Im Neuenheimer Feld 280, Heidelberg 69120, Germany.
authors.forename: Marc
authors.initials: M
authors.lastname: Kachelrieß
mesh_terms: D016477:Artifacts; D003198:Computer Simulation; D054893:Cone-Beam Computed Tomography / Q000295:instrumentation* / Q000379:methods*; D004867:Equipment Design; D006257:Head / Q000000981:diagnostic imaging; D006801:Humans; D021621:Imaging, Three-Dimensional / Q000295:instrumentation* / Q000379:methods*; D008953:Models, Anatomic; D019047:Phantoms, Imaging; D012399:Rotation