Continuous Analog of Accelerated OS-EM Algorithm for Computed Tomography
- Resource Type
- Authors
- Yusaku Yamaguchi; Tetsuya Yoshinaga; Kiyoko Tateishi; Omar M. Abou Al-Ola
- Source
- Mathematical Problems in Engineering, Vol 2017 (2017)
- Subject
- Article Subject
Discretization
Differential equation
General Mathematics
lcsh:Mathematics
Mathematical analysis
General Engineering
02 engineering and technology
Iterative reconstruction
Inverse problem
lcsh:QA1-939
030218 nuclear medicine & medical imaging
03 medical and health sciences
Nonlinear system
0302 clinical medicine
Rate of convergence
lcsh:TA1-2040
0202 electrical engineering, electronic engineering, information engineering
Piecewise
020201 artificial intelligence & image processing
Vector field
lcsh:Engineering (General). Civil engineering (General)
Mathematics
- Language
- English
- ISSN
- 1563-5147
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.