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Convergence analysis of an accelerated expectation‐maximization algorithm for ill‐posed integral equations
Author(s) -
Geng Chuanxing,
Wang Jinping
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3508
Subject(s) - expectation–maximization algorithm , convergence (economics) , mathematics , algorithm , acceleration , rate of convergence , focus (optics) , maximization , mathematical optimization , maximum likelihood , computer science , key (lock) , statistics , physics , computer security , classical mechanics , optics , economics , economic growth
The maximum‐likelihood expectation‐maximization (EM) algorithm has attracted considerable interest in single‐photon emission computed tomography, because it produces superior images in addition to be being flexible, simple, and allowing a physical interpretation. However, it often needs a large number of calculations because of the algorithm's slow rate of convergence. Therefore, there is a large body of literature concerning the EM algorithm's acceleration. One of the accelerated means is increasing an overrelaxation parameter, whereas we have not found any analysis in this method that would provide an immediate answer to the questions of the convergence. In this paper, our main focus is on the continuous version of an accelerated EM algorithm based on Lewitt and Muehllenner. We extend their conclusions to the infinite‐dimensional space and interpret and analyze the convergence of the accelerated EM algorithm. We also obtain some new properties of the modified algorithm. Copyright © 2015 John Wiley & Sons, Ltd.