Continuous analog of accelerated OS-EM algorithm for computed tomography
type: Item
instance of: scholarly article
title: Continuous analog of accelerated OS-EM algorithm for computed tomography
zbMATH Open document ID: 1426.94024
DOI: 10.1155/2017/1564123
author: Kiyoko Tateishi
author: Yusaku Yamaguchi
author: Omar M. Abou Al-Ola
author: Tetsuya Yoshinaga
published in: Mathematical Problems in Engineering
publication date: 2018-11-05T00:00:00Z
review text: Summary: The maximum-likelihood expectation-maximization (ML-EM) algorithm is used for an iterative image reconstruction (IIR) method and performs well with respect to the inverse problem as cross-entropy minimization in computed tomography. For accelerating the convergence rate of the ML-EM, the ordered-subsets expectation-maximization (OS-EM) with a power factor is effective. In this paper, we propose a continuous analog to the power-based accelerated OS-EM algorithm. The continuous-time image reconstruction (CIR) system is described by nonlinear differential equations with piecewise smooth vector fields by a cyclic switching process. A numerical discretization of the differential equation by using the geometric multiplicative first-order expansion of the nonlinear vector field leads to an exact equivalent iterative formula of the power-based OS-EM. The convergence of nonnegatively constrained solutions to a globally stable equilibrium is guaranteed by the Lyapunov theorem for consistent inverse problems. We illustrate through numerical experiments that the convergence characteristics of the continuous system have the highest quality compared with that of discretization methods. We clarify how important the discretization method approximates the solution of the CIR to design a better IIR method.
Mathematics Subject Classification ID: 94A08
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 92C55
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 65L09
zbMATH DE Number: 6971761
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/1564123
OpenAlex ID: W2743120499
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description: scientific article; zbMATH DE number 6971761