Convergence analysis of an accelerated expectation-maximization algorithm for ill-posed integral equations. (English) Zbl 1339.65250
Authors’ abstract: 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.
Reviewer: Mikhail Yu. Kokurin (Yoshkar-Ola)
MSC:
| 65R30 | Numerical methods for ill-posed problems for integral equations |
| 65F22 | Ill-posedness and regularization problems in numerical linear algebra |
| 47A52 | Linear operators and ill-posed problems, regularization |
| 65R20 | Numerical methods for integral equations |
| 45B05 | Fredholm integral equations |
Keywords:
convergence; acceleration; maximum-likelihood expectation-maximization algorithm; single-photon emission computed tomography; overrelaxationReferences:
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