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基于离散路径积分和高效公式的光学层析成像的原始对偶方法。

Primal-dual approach to optical tomography with discretized path integral with efficient formulations.

作者信息

Yuan Bingzhi, Tamaki Toru, Raytchev Bisser, Kaneda Kazufumi

机构信息

Hiroshima University, Department of Information Engineering, Graduate School of Engineering, Higashi-Hiroshima, Japan.

出版信息

J Med Imaging (Bellingham). 2017 Jul;4(3):033501. doi: 10.1117/1.JMI.4.3.033501. Epub 2017 Jul 19.

DOI:10.1117/1.JMI.4.3.033501
PMID:28744477
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC5516095/
Abstract

We propose an efficient optical tomography with discretized path integral. We first introduce the primal-dual approach to solve the inverse problem formulated as a constraint optimization problem. Next, we develop efficient formulations for computing Jacobian and Hessian of the cost function of the constraint nonlinear optimization problem. Numerical experiments show that the proposed formulation is faster ([Formula: see text]) than the previous work with the log-barrier interior point method ([Formula: see text]) for the Shepp-Logan phantom with a grid size of [Formula: see text], while keeping the quality of the estimation results (root-mean-square error increasing by up to 12%).

摘要

我们提出了一种基于离散路径积分的高效光学层析成像方法。我们首先引入原对偶方法来求解被表述为约束优化问题的逆问题。接下来，我们为计算约束非线性优化问题的代价函数的雅可比矩阵和海森矩阵开发了高效的公式。数值实验表明，对于网格大小为[公式：见原文]的Shepp-Logan体模，所提出的公式比使用对数障碍内点法的先前工作更快（[公式：见原文]），同时保持估计结果的质量（均方根误差最多增加12%）。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/dc5e/5516095/83ec7e3973a1/JMI-004-033501-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/dc5e/5516095/ca1498fbad1a/JMI-004-033501-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/dc5e/5516095/71d38f215b12/JMI-004-033501-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/dc5e/5516095/cbd9f311bd55/JMI-004-033501-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/dc5e/5516095/83ec7e3973a1/JMI-004-033501-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/dc5e/5516095/ca1498fbad1a/JMI-004-033501-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/dc5e/5516095/71d38f215b12/JMI-004-033501-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/dc5e/5516095/cbd9f311bd55/JMI-004-033501-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/dc5e/5516095/83ec7e3973a1/JMI-004-033501-g004.jpg

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