title: Completeness map evaluation demonstrated with candidate next-generation cardiac CT architectures.
abstract: OBJECTIVE
  In this report, the authors introduce the general concept of the completeness map, as a means to evaluate the completeness of data acquired by a given CT system design (architecture and scan mode). They illustrate the utility of completeness map by applying the completeness map concept to a number of candidate CT system designs, as part of a study to advance the state-of-the-art in cardiac CT.
  
  
  METHODS
  In order to optimally reconstruct a point within a volume of interest (VOI), the Radon transform on all possible planes through that point should be measured. The authors quantified the extent to which this ideal condition is satisfied for the entire image volume. They first determined a Radon completeness number for each point in the VOI, as the percentage of possible planes that is actually measured. A completeness map is then defined as a 3D matrix of the completeness numbers for the entire VOI. The authors proposed algorithms to analyze the projection datasets in Radon space and compute the completeness number for a fixed point and apply these algorithms to various architectures and scan modes that they are evaluating. In this report, the authors consider four selected candidate architectures, operating with different scan modes, for a total of five system design alternatives. Each of these alternatives is evaluated using completeness map.
  
  
  RESULTS
  If the detector size and cone angle are large enough to cover the entire cardiac VOI, a single-source circular scan can have ≥99% completeness over the entire VOI. However, only the central z-slice can be exactly reconstructed, which corresponds to 100% completeness. For a typical single-source architecture, if the detector is limited to an axial dimension of 40 mm, a helical scan needs about five rotations to form an exact reconstruction region covering the cardiac VOI, while a triple-source helical scan only requires two rotations, leading to a 2.5x improvement in temporal resolution. If the source and detector of an inverse-geometry (IGCT) system have the same axial extent, and the spacing of source points in the axial and transaxial directions is sufficiently small, the IGCT can also form an exact reconstruction region for the cardiac VOI. If the VOI can be covered by the x-ray beam in any view, a composite-circling scan can generate an exact reconstruction region covering the VOI.
  
  
  CONCLUSIONS
  The completeness map evaluation provides useful information for selecting the next-generation cardiac CT system design. The proposed completeness map method provides a practical tool for analyzing complex scanning trajectories, where the theoretical image quality for some complex system designs is impossible to predict, without yet-undeveloped reconstruction algorithms.
authors.affiliation: Department of Radiology, Wake Forest University Health Sciences, Winston-Salem, NC 27157, USA.
authors.forename: Baodong
authors.initials: B
authors.lastname: Liu
authors.forename: James
authors.initials: J
authors.lastname: Bennett
authors.forename: Ge
authors.initials: G
authors.lastname: Wang
authors.forename: Bruno
authors.initials: B
authors.lastname: De Man
authors.forename: Kai
authors.initials: K
authors.lastname: Zeng
authors.forename: Zhye
authors.initials: Z
authors.lastname: Yin
authors.forename: Paul
authors.initials: P
authors.lastname: Fitzgerald
authors.forename: Hengyong
authors.initials: H
authors.lastname: Yu
mesh_terms: D004867:Equipment Design; D006321:Heart / Q000000981:diagnostic imaging*; D014057:Tomography, X-Ray Computed / Q000295:instrumentation / Q000379:methods*