Fast gradient-based methods for Bayesian reconstruction of transmission and emission PET images

Erkan U. Mumcuoglu, Richard Leahy, Simon R. Cherry, Zhenyu Zhou

Research output: Contribution to journalArticlepeer-review

201 Scopus citations


We describe conjugate gradient algorithms for reconstruction of transmission and emission PET images. The reconstructions are based on a Bayesian formulation, where the data are modeled as a collection of independent Poisson random variables and the image is modeled using a Markov random field. A conjugate gradient algorithm is used to compute a maximum a posteriori (MAP) estimate of the image by maximizing over the posterior density. To ensure nonnegativity of the solution, a penalty function is used to convert the problem to one of unconstrained optimization. Preconditioners are used to enhance convergence rates. These methods generally achieve effective convergence in 15-25 iterations. Reconstructions are presented of an 18FDG whole body scan from data collected using a Siemens/CTI ECAT931 whole body system. These results indicate significant improvements in emission image quality using the Bayesian approach, in comparison to filtered backprojection, particularly when reprojections of the MAP transmission image are used in place of the standard attenuation correction factors.

Original languageEnglish (US)
Pages (from-to)687-701
Number of pages15
JournalIEEE Transactions on Medical Imaging
Issue number4
StatePublished - Dec 1994
Externally publishedYes

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Biomedical Engineering
  • Electrical and Electronic Engineering
  • Radiology Nuclear Medicine and imaging
  • Radiological and Ultrasound Technology


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