Fast proximity algorithm for MAP ECT reconstruction

Si Li, Andrzej Krol, Lixin Shen, Yuesheng Xu

Research output: Chapter in Book/Entry/PoemConference contribution


We arrived at the fixed-point formulation of the total variation maximum a posteriori (MAP) regularized emission computed tomography (ECT) reconstruction problem and we proposed an iterative alternating scheme to numerically calculate the fixed point. We theoretically proved that our algorithm converges to unique solutions. Because the obtained algorithm exhibits slow convergence speed, we further developed the proximity algorithm in the transformed image space, i.e. the preconditioned proximity algorithm. We used the bias-noise curve method to select optimal regularization hyperparameters for both our algorithm and expectation maximization with total variation regularization (EM-TV). We showed in the numerical experiments that our proposed algorithms, with an appropriately selected preconditioner, outperformed conventional EM-TV algorithm in many critical aspects, such as comparatively very low noise and bias for Shepp-Logan phantom. This has major ramification for nuclear medicine because clinical implementation of our preconditioned fixed-point algorithms might result in very significant radiation dose reduction in the medical applications of emission tomography.

Original languageEnglish (US)
Title of host publicationMedical Imaging 2012
Subtitle of host publicationPhysics of Medical Imaging
StatePublished - 2012
EventMedical Imaging 2012: Physics of Medical Imaging - San Diego, CA, United States
Duration: Feb 5 2012Feb 8 2012

Publication series

NameProgress in Biomedical Optics and Imaging - Proceedings of SPIE
ISSN (Print)1605-7422


OtherMedical Imaging 2012: Physics of Medical Imaging
Country/TerritoryUnited States
CitySan Diego, CA


  • MAP ECT reconstruction
  • fixed-point
  • preconditioned proximity algorithm
  • total variation regularization

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Radiology Nuclear Medicine and imaging
  • Biomaterials


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