title: Multigrid reconstruction with block-iterative updates for breast tomosynthesis.
abstract: OBJECTIVE
  The authors wish to evaluate the possible advantages of using a multigrid approach to maximum-a-posteriori reconstruction in digital breast tomosynthesis together with block-iterative updates in the form of either plane-by-plane updates or ordered subsets.
  
  
  METHODS
  The authors previously developed a penalized maximum likelihood reconstruction algorithm with resolution model dedicated to breast tomosynthesis [K. Michielsen et al., "Patchwork reconstruction with resolution modeling for digital breast tomosynthesis," Med. Phys. 40, 031105 (10pp.) (2013)]. This algorithm was extended with ordered subsets and multigrid updates, and the effects on the convergence and on limited angle artifact appearance were evaluated on a mathematical phantom and patient data. To ensure a fair comparison, the analysis was performed at the same computational cost for all methods. To assess convergence and artifact creation in the phantom reconstructions, the authors looked at posterior likelihood, sum of squared residuals, contrast of identical calcifications at different positions, and the standard deviation between the contrasts of these calcifications. For the patient cases, the authors calculated posterior likelihood, measured the signal difference to noise ratio of subtle microcalcifications, and visually evaluated the reconstructions.
  
  
  RESULTS
  The authors selected multigrid sequences scoring in the best 10% of the four evaluated parameters, except for the reconstructions with subsets where a low standard deviation of the contrast was incompatible with the three other parameters. In further evaluation of phantom reconstructions from noisy data and patient data, the authors found improved convergence and a reduction in artifacts for our chosen multigrid reconstructions compared to the single grid reconstructions with equivalent computational cost, although there was a diminishing return for an increasing number of subsets.
  
  
  CONCLUSIONS
  Multigrid reconstruction improves upon reconstruction with a fixed grid when evaluated at a fixed computational cost. For multigrid reconstruction, using plane-by-plane updates or applying ordered subsets resulted in similar performance.
authors.affiliation: Department of Imaging and Pathology, Division of Nuclear Medicine and Molecular Imaging, KU Leuven, Leuven 3000, Belgium and Medical Imaging Research Center, KU Leuven, Leuven 3000, Belgium.
authors.forename: Koen
authors.initials: K
authors.lastname: Michielsen
authors.affiliation: Department of Imaging and Pathology, Division of Nuclear Medicine and Molecular Imaging, KU Leuven, Leuven 3000, Belgium and Medical Imaging Research Center, KU Leuven, Leuven 3000, Belgium.
authors.forename: Johan
authors.initials: J
authors.lastname: Nuyts
mesh_terms: D000465:Algorithms; D001943:Breast Neoplasms / Q000000981:diagnostic imaging*; D005260:Female; D006801:Humans; D021621:Imaging, Three-Dimensional / Q000295:instrumentation / Q000379:methods*; D008327:Mammography / Q000295:instrumentation / Q000379:methods*; D019047:Phantoms, Imaging; D011856:Radiographic Image Enhancement / Q000379:methods; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D014057:Tomography, X-Ray Computed / Q000295:instrumentation / Q000379:methods*