TY - JOUR

T1 - String-averaging expectation-maximization for maximum likelihood estimation in emission tomography

AU - Helou, Elias Salomão

AU - Censor, Yair

AU - Chen, Tai Been

AU - Chern, I. Liang

AU - De Pierro, Álvaro Rodolfo

AU - Jiang, Ming

AU - Lu, Henry Horng Shing

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

KW - blockiterative

KW - expectation-maximization (EM) algorithm

KW - ordered subsets expectation maximization (OSEM) algorithm, relaxed EM

KW - positron emission tomography (PET)

KW - string-averaging

KW - string-averaging EM algorithm

UR - http://www.scopus.com/inward/record.url?scp=84899724242&partnerID=8YFLogxK

U2 - 10.1088/0266-5611/30/5/055003

DO - 10.1088/0266-5611/30/5/055003

M3 - Article

AN - SCOPUS:84899724242

SN - 0266-5611

VL - 30

JO - Inverse Problems

JF - Inverse Problems

IS - 5

M1 - 055003

ER -