String-averaging expectation-maximization for maximum likelihood estimation in emission tomography

Elias Salomão Helou, Yair Censor, Tai Been Chen, I. Liang Chern, Álvaro Rodolfo De Pierro, Ming Jiang, Henry Horng Shing Lu

Research output: Contribution to journalArticlepeer-review


We study the maximum likelihood model in emission tomography and propose a new family of algorithms for its solution, called string-averaging expectation-maximization (SAEM). In the string-averaging algorithmic regime, the index set of all underlying equations is split into subsets, called 'strings', and the algorithm separately proceeds along each string, possibly in parallel. Then, the end-points of all strings are averaged to form the next iterate. SAEM algorithms with several strings present better practical merits than the classical row-action maximum-likelihood algorithm. We present numerical experiments showing the effectiveness of the algorithmic scheme, using data of image reconstruction problems. Performance is evaluated from the computational cost and reconstruction quality viewpoints. A complete convergence theory is also provided.

Original languageEnglish
Article number055003
JournalInverse Problems
Issue number5
StatePublished - May 2014


  • blockiterative
  • expectation-maximization (EM) algorithm
  • ordered subsets expectation maximization (OSEM) algorithm, relaxed EM
  • positron emission tomography (PET)
  • string-averaging
  • string-averaging EM algorithm

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics


Dive into the research topics of 'String-averaging expectation-maximization for maximum likelihood estimation in emission tomography'. Together they form a unique fingerprint.

Cite this