title: Noise properties of CT images reconstructed by use of constrained total-variation, data-discrepancy minimization.
abstract: OBJECTIVE
  The authors develop and investigate iterative image reconstruction algorithms based on data-discrepancy minimization with a total-variation (TV) constraint. The various algorithms are derived with different data-discrepancy measures reflecting the maximum likelihood (ML) principle. Simulations demonstrate the iterative algorithms and the resulting image statistical properties for low-dose CT data acquired with sparse projection view angle sampling. Of particular interest is to quantify improvement of image statistical properties by use of the ML data fidelity term.
  
  
  METHODS
  An incremental algorithm framework is developed for this purpose. The instances of the incremental algorithms are derived for solving optimization problems including a data fidelity objective function combined with a constraint on the image TV. For the data fidelity term the authors, compare application of the maximum likelihood principle, in the form of weighted least-squares (WLSQ) and Poisson-likelihood (PL), with the use of unweighted least-squares (LSQ).
  
  
  RESULTS
  The incremental algorithms are applied to projection data generated by a simulation modeling the breast computed tomography (bCT) imaging application. The only source of data inconsistency in the bCT projections is due to noise, and a Poisson distribution is assumed for the transmitted x-ray photon intensity. In the simulations involving the incremental algorithms an ensemble of images, reconstructed from 1000 noise realizations of the x-ray transmission data, is used to estimate the image statistical properties. The WLSQ and PL incremental algorithms are seen to reduce image variance as compared to that of LSQ without sacrificing image bias. The difference is also seen at few iterations--short of numerical convergence of the corresponding optimization problems.
  
  
  CONCLUSIONS
  The proposed incremental algorithms prove effective and efficient for iterative image reconstruction in low-dose CT applications particularly with sparse-view projection data.
authors.affiliation: Department of Radiology, University of Chicago, 5841 South Maryland Avenue, Chicago, Illinois 60637.
authors.forename: Sean
authors.initials: S
authors.lastname: Rose
authors.affiliation: Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby 2800, Denmark.
authors.forename: Martin S
authors.initials: MS
authors.lastname: Andersen
authors.affiliation: Department of Radiology, University of Chicago, 5841 South Maryland Avenue, Chicago, Illinois 60637.
authors.forename: Emil Y
authors.initials: EY
authors.lastname: Sidky
authors.affiliation: Department of Radiology, University of Chicago, 5841 South Maryland Avenue, Chicago, Illinois 60637.
authors.forename: Xiaochuan
authors.initials: X
authors.lastname: Pan
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D006801:Humans; D016018:Least-Squares Analysis; D016013:Likelihood Functions; D008327:Mammography / Q000379:methods; D017785:Photons; D016012:Poisson Distribution; D014057:Tomography, X-Ray Computed / Q000379:methods*; D014965:X-Rays