String-Averaging Expectation-Maximization for Maximum Likelihood Estimation in Emission Tomography
Elias S. Helou Helou(eliasicmc.usp.br)
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.
Entry Submitted: 02/05/2014
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