Semi-dynamic preconditioned alternating projection MAP ECT reconstruction from low-dose ECT

Andrzej Krol, Si Li, Yuesheng Xu, Jiahan Zhang, Levon O. Vogelsang, Lixin Shen, David H. Feiglin

Research output: Chapter in Book/Entry/PoemConference contribution


The objective of this study was to develop very low noise and high-contrast-to-noise ratio fast proximity algorithm for MAP ECT reconstruction that would allow significant (factor of two or more) patient's dose reduction, as compared to conventional OSEM algorithm. We proposed a semi-dynamic Preconditioned Alternating Projection Algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulated the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We characterized the solution of the constrained convex optimization problem and showed that it satisfies a system of fixed-point equations defined in terms of two proximity operators arising from the convex functions that define the TV-norm and the constrain involved in the problem. We proved theoretically the convergence of the proposed algorithm. For efficient numerical computation, we introduced to the alternating projection algorithm a preconditioning matrix: the EM-preconditioner. In numerical experiments using Monte Carlo simulated SPECT data performance of our algorithms was compared with performance of the conventional EM algorithm with Gaussian postfilter. Based on the results of these experiments, we observed that PAPA algorithm with the EM-preconditioner outperforms very significantly the benchmark EM in terms of contrast-to-noise ratio and the noise characteristics of the reconstructed images.

Original languageEnglish (US)
Title of host publicationMedical Imaging 2013
Subtitle of host publicationPhysics of Medical Imaging
StatePublished - 2013
Externally publishedYes
EventMedical Imaging 2013: Physics of Medical Imaging - Lake Buena Vista, FL, United States
Duration: Feb 11 2013Feb 14 2013

Publication series

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


OtherMedical Imaging 2013: Physics of Medical Imaging
Country/TerritoryUnited States
CityLake Buena Vista, FL


  • MAP SPECT reconstruction
  • Preconditioned alternating projection algorithm
  • Semi dynamic EM preconditioner

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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