continuous analog of accelerated os-em algorithm for computed tomography

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ID: 234254
2017
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Abstract
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.
Reference Key
tateishi2017mathematicalcontinuous Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Kiyoko Tateishi;Yusaku Yamaguchi;Omar M. Abou Al-Ola;Tetsuya Yoshinaga
Journal journal of power sources
Year 2017
DOI
10.1155/2017/1564123
URL
http://dx.doi.org/10.1155/2017/1564123
Keywords
civil engineering (general)mathematics engineering (general)

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