title: Homotopic non-local regularized reconstruction from sparse positron emission tomography measurements.
abstract: BACKGROUND
  Positron emission tomography scanners collect measurements of a patient's in vivo radiotracer distribution. The system detects pairs of gamma rays emitted indirectly by a positron-emitting radionuclide (tracer), which is introduced into the body on a biologically active molecule, and the tomograms must be reconstructed from projections. The reconstruction of tomograms from the acquired PET data is an inverse problem that requires regularization. The use of tightly packed discrete detector rings, although improves signal-to-noise ratio, are often associated with high costs of positron emission tomography systems. Thus a sparse reconstruction, which would be capable of overcoming the noise effect while allowing for a reduced number of detectors, would have a great deal to offer.
  
  
  METHODS
  In this study, we introduce and investigate the potential of a homotopic non-local regularization reconstruction framework for effectively reconstructing positron emission tomograms from such sparse measurements.
  
  
  RESULTS
  Results obtained using the proposed approach are compared with traditional filtered back-projection as well as expectation maximization reconstruction with total variation regularization.
  
  
  CONCLUSIONS
  A new reconstruction method was developed for the purpose of improving the quality of positron emission tomography reconstruction from sparse measurements. We illustrate that promising reconstruction performance can be achieved for the proposed approach even at low sampling fractions, which allows for the use of significantly fewer detectors and have the potential to reduce scanner costs.
authors.affiliation: Department of Systems Design Engineering, University of Waterloo, Waterloo, Ontario, Canada. Alex.S.Wong@gmail.com.
authors.forename: Alexander
authors.initials: A
authors.lastname: Wong
authors.affiliation: Department of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, China. liucheny@gmail.com.
authors.forename: Chenyi
authors.initials: C
authors.lastname: Liu
authors.affiliation: Department of Systems Design Engineering, University of Waterloo, Waterloo, Ontario, Canada. x18wang@uwaterloo.ca.
authors.forename: Xiao Yu
authors.initials: XY
authors.lastname: Wang
authors.affiliation: Department of Systems Design Engineering, University of Waterloo, Waterloo, Ontario, Canada. pfieguth@uwaterloo.ca.
authors.forename: Paul
authors.initials: P
authors.lastname: Fieguth
authors.affiliation: Department of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, China. biehx@bupt.edu.cn.
authors.forename: Hongxia
authors.initials: H
authors.lastname: Bie
mesh_terms: D000465:Algorithms; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D049268:Positron-Emission Tomography / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity