Continuous Analog of Accelerated OS-EM Algorithm for Computed Tomography

Tateishi Kiyoko; Yamaguchi Yusaku; Abou Al-Ola Omar M.; Yoshinaga Tetsuya

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Continuous Analog of Accelerated OS-EM Algorithm for Computed Tomography

机译：计算机断层扫描的加速OS-EM算法的连续模拟

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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 IIRmethod.

机译：最大似然期望最大化（ML-EM）算法用于迭代图像重建（IIR）方法，并且在计算机断层扫描中作为交叉熵最小化的逆问题表现良好。为了加快ML-EM的收敛速度，具有功率因数的有序子集期望最大化（OS-EM）是有效的。在本文中，我们提出了基于功率的加速OS-EM算法的连续模拟。连续时间图像重建（CIR）系统由非线性微分方程组成，具有分段光滑矢量场，并通过循环切换过程进行描述。通过使用非线性矢量场的几何乘法一阶展开对微分方程进行数值离散，可以得出基于功率的OS-EM的精确等效迭代公式。关于一致反问题的李雅普诺夫定理保证了非负约束解到全局稳定均衡的收敛。通过数值实验表明，与离散化方法相比，连续系统的收敛特性具有最高的质量。我们阐明了离散化方法近似CIR解决方案以设计更好的IIR方法的重要性。

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《Mathematical Problems in Engineering》 |2017年第7期|1564123.1-1564123.8|共8页
作者
Tateishi Kiyoko; Yamaguchi Yusaku; Abou Al-Ola Omar M.; Yoshinaga Tetsuya;
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Tokushima Univ, Grad Sch Hlth Sci, 3-18-15 Kuramoto, Tokushima 7708509, Japan;

Shikoku Med Ctr Children & Adults, 2-1-1 Senyu, Zentsuji 7658507, Japan;

Tanta Univ, Fac Sci, El Giesh St, Tanta 31527, Gharbia, Egypt;

Tokushima Univ, Inst Biomed Sci, 3-18-15 Kuramoto, Tokushima 7708509, Japan;

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1. Interest of the ordered subsets expectation maximization (OS-EM) algorithm in pinhole single-photon emission tomography reconstruction: a phantom study. [J] . Vanhove C, Defrise M, Franken PR, European journal of nuclear medicine . 2000,第2期

机译：针孔单光子发射层析成像重建中有序子集期望最大化（OS-EM）算法的兴趣：幻像研究。
2. A comparative study of an X-ray tomography reconstruction algorithm in accelerated and cloud computing systems [J] . Estefania Serrano, Javier Garcia Blas, Jesus Carretero Concurrency, practice and experience . 2015,第18期

机译：加速和云计算系统中X射线断层扫描重建算法的比较研究
3. Globally accelerated reconstruction algorithm for diffusion tomography with continuous-wave source in an arbitrary convex shape domain [J] . Natee Pantong, Jianzhong Su, Hua Shan, Journal of the Optical Society of America, A. Optics, image science, and vision . 2009,第3期

机译：任意凸形域连续波源扩散层析成像的全局加速重建算法
4. Continuous analog of multiplicative algebraic reconstruction technique for computed tomography [C] . Kiyoko Tateishi, Yusaku Yamaguchi, Omar M. Abou Al-Ola, Conference on physics of medical imaging . 2016

机译：计算机断层扫描的乘法代数重建技术的连续模拟
5. Accelerated optimization algorithms for statistical 3D x-ray computed tomography image reconstruction. [D] . Kim, Donghwan. 2014

机译：统计3D X射线计算机断层扫描图像重建的加速优化算法。
6. Registration of planar bioluminescence to magnetic resonance and x-ray computed tomography images as a platform for the development of bioluminescence tomography reconstruction algorithms [O] . Bradley J. Beattie, Alexander D. Klose, Carl H. Le, 2009

机译：将平面生物发光配准到磁共振和X射线计算机断层摄影图像作为开发生物发光断层摄影重建算法的平台
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Continuous Analog of Accelerated OS-EM Algorithm for Computed Tomography

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