A new non-monotonic algorithm for PET image reconstruction

Suvrit Sra, Dongmin Kim, Inderjit Dhillon, Bernhard Schölkopf

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

Maximizing some form of Poisson likelihood (either with or without penalization) is central to image reconstruction algorithms in emission tomography. In this paper we introduce NMML, a non-monotonic algorithm for maximum likelihood PET image reconstruction. NMML offers a simple and flexible procedure that also easily incorporates standard convex regularization for doing penalized likelihood estimation. A vast number image reconstruction algorithms have been developed for PET, and new ones continue to be designed. Among these, methods based on the expectation maximization (EM) and ordered-subsets (OS) framework seem to have enjoyed the greatest popularity. Our method NMML differs fundamentally from methods based on EM: i) it does not depend on the concept of optimization transfer (or surrogate functions); and ii) it is a rapidly converging nonmonotonic descent procedure. The greatest strengths of NMML, however, are its simplicity, efficiency, and scalability, which make it especially attractive for tomographic reconstruction. We provide a theoretical analysis NMML, and empirically observe it to outperform standard EM based methods, sometimes by orders of magnitude. NMML seamlessly allows integreation of penalties (regularizers) in the likelihood. This ability can prove to be crucial, especially because with the rapidly rising importance of combined PET/MR scanners, one will want to include more "prior" knowledge into the reconstruction.

Original languageEnglish
Title of host publication2009 IEEE Nuclear Science Symposium Conference Record, NSS/MIC 2009
Pages2500-2502
Number of pages3
DOIs
StatePublished - 2009
Externally publishedYes
Event2009 IEEE Nuclear Science Symposium Conference Record, NSS/MIC 2009 - Orlando, FL, United States
Duration: 25 Oct 200931 Oct 2009

Publication series

NameIEEE Nuclear Science Symposium Conference Record
ISSN (Print)1095-7863

Conference

Conference2009 IEEE Nuclear Science Symposium Conference Record, NSS/MIC 2009
Country/TerritoryUnited States
CityOrlando, FL
Period25/10/0931/10/09

Keywords

  • Convex optimization
  • Emission tomography
  • Non-monotonic maximum likelihood
  • Ordered subsets expectation maximization (OS-EM)
  • Penalized likelihood
  • Transmission tomography

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