2001
DOI: 10.1109/42.921477
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Fast EM-like methods for maximum "a posteriori" estimates in emission tomography

Abstract: The maximum-likelihood (ML) approach in emission tomography provides images with superior noise characteristics compared to conventional filtered backprojection (FBP) algorithms. The expectation-maximization (EM) algorithm is an iterative algorithm for maximizing the Poisson likelihood in emission computed tomography that became very popular for solving the ML problem because of its attractive theoretical and practical properties. Recently, (Browne and DePierro, 1996 and Hudson and Larkin, 1994) block sequenti… Show more

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Cited by 141 publications
(121 citation statements)
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“…Algorithm (6) is correspondingly named the superiorized version of Algorithm (4). Notice that if we definẽ…”
Section: Algorithm Descriptionmentioning
confidence: 99%
See 1 more Smart Citation
“…Algorithm (6) is correspondingly named the superiorized version of Algorithm (4). Notice that if we definẽ…”
Section: Algorithm Descriptionmentioning
confidence: 99%
“…, x n are the components of x. Each of these operators is no more than a block-ramla (bramla) iteration over a specific data subset [2,4]. A bramla iteration is a generalization of a ramla iteration whereby blocks of data can be used at each subiteration.…”
Section: String-averaging Expectation Maximizationmentioning
confidence: 99%
“…These algorithms are used without any modifications, however we mention these algorithms in this section for completeness. Alternatives for energy minimization include gradient descent (Hansis et al, 2009), stochastic gradient descent (Rohkohl et al, 2009a(Rohkohl et al, , 2010a, L-BFGS-B (Rohkohl et al, 2009b(Rohkohl et al, , 2010b, separable paraboloidal surrogates (SPS) (Erdogan and Fessler, 1999;Hu et al, 2010Hu et al, , 2012, and block sequential regularized expectation maximization (BSREM) (de Pierro and Beleza Yamagishi, 2001;Zhou et al, 2008).…”
Section: Specialized Tomographic Reconstruction Algorithmsmentioning
confidence: 99%
“…9,10 Despite their success in speeding up the initial convergence, ordinary OS algorithms are not convergent in general but rather approach a suboptimal limit-cycle without relaxation, i.e., when α n = α. To address this issue, several families of convergent OS type algorithms have been proposed, [11][12][13][14] although those modifications tend to slow down convergence. In this paper, we focus on the initial convergence characteristics of OS algorithms rather than their final convergence properties.…”
Section: Ordered-subsets (Os) Algorithmsmentioning
confidence: 99%