title: A new redundancy weighting scheme for nonstationary data for computed tomography.
abstract: OBJECTIVE
  The same projection data (or line integrals) are often measured multiple times, e.g., twice from opposite directions during one gantry rotation. The redundant data must be normalized by applying redundancy weighting such as the halfscan algorithm, which assumes that the noise of the data is uniform. This assumption, however, is not correct when a tube current modulation technique is employed. The variance of line integrals, which is inversely related to the tube current, could vary significantly. The purpose of this work is to improve how the projection data are used during analytical reconstruction when the tube current is modulated during the scan.
  
  
  METHODS
  The authors developed a new redundancy weighting scheme. It not only takes into account the data statistics but also can control how much to weigh the statistics from 100% (αs = 1.0) to 0% (αs = 0.0) by a parameter αs. The proposed weighting scheme reduces to the conventional redundancy weighting scheme when αs = 0.0. The authors evaluated the performance of the proposed scheme using computer simulations targeting at myocardial perfusion CT imaging. The image quality was evaluated in terms of the image noise and halfscan artifacts, and perfusion defect detection performance was evaluated by the positive predictive value (PPV) and the area-under-the-receiver operating characteristic-curve (AUC) value.
  
  
  RESULTS
  Results showed a tradeoff between the image noise and halfscan artifacts. The normalized noise standard deviation was 1.00 with halfscan, 0.89 with αs = 1.0, 0.97 with αs = 0.5, and 1.20 with αs = 0.0 when projections over one rotation (75% of projections are acquired with full dose, 25% with 1/10 of the full dose) are used. The halfscan artifacts were 13.4 Hounsfield unit (HU) with halfscan, 8.2 HU with αs = 1.0, 4.5 HU with αs = 0.5, and 3.1 HU with αs = 0.0. Both the PPVs and AUCs were improved from the halfscan method: PPV, 69.0%-70.6% vs 58.0%, P < 0.003; AUC, 0.935-0.938 vs 0.908, P < 0.003.
  
  
  CONCLUSIONS
  The new redundancy weight allows for decreasing the image noise and controlling the tradeoff between the image noise and artifacts.
authors.affiliation: Division of Medical Imaging Physics, The Russell H. Morgan Department of Radiology and Radiological Science, Johns Hopkins University School of Medicine, Baltimore, Maryland 21287.
authors.forename: Katsuyuki
authors.initials: K
authors.lastname: Taguchi
authors.affiliation: Division of Medical Imaging Physics, The Russell H. Morgan Department of Radiology and Radiological Science, Johns Hopkins University School of Medicine, Baltimore, Maryland 21287.
authors.forename: Jochen
authors.initials: J
authors.lastname: Cammin
mesh_terms: D019540:Area Under Curve; D016477:Artifacts; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006321:Heart / Q000000981:diagnostic imaging; D006801:Humans; D055414:Myocardial Perfusion Imaging / Q000379:methods; D012372:ROC Curve; D014057:Tomography, X-Ray Computed / Q000379:methods*