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String-Averaging Expectation-Maximization for Maximum Likelihood Estimation in Emission Tomography

Elias S. Helou Helou(elias***at***icmc.usp.br)
Yair Censor(yair***at***math.haifa.ac.il)
Tai-Been Chen(ctb***at***isu.edu.tw)
I-Liang Chern(chern***at***math.ntu.edu.tw)
Álvaro Rodolfo De Pierro(alvaro***at***ime.unicamp.br)
Ming Jiang(ming-jiang***at***ieee.org)
Henry Horng-Shing Lu(hslu***at***stat.nctu.edu.tw)

Abstract: 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 presents better practical merits than the classical Row-Action Maximum-Likelihood Algorithm (RAMLA). We present numerical experiments showing the effectiveness of the algorithmic scheme in realistic situations. Performance is evaluated from the computational cost and reconstruction quality viewpoints. A complete convergence theory is also provided.

Keywords: Emission tomography (ET), String-averaging, Block-iterative, Expectation maximization (EM) algorithm, Ordered subsets expectation maximization (OSEM) algorithm, Relaxed EM, String-averaging EM algorithm.

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Applications -- Science and Engineering (Biomedical Applications )

Citation: Inverse Problems, accepted for publication.

Download: [PDF]

Entry Submitted: 02/05/2014
Entry Accepted: 02/05/2014
Entry Last Modified: 02/05/2014

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