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A comparison of alternating minimization and expectation maximization algorithms for single source gamma ray tomography

机译：单源伽马射线断层扫描的交替最小化和期望最大化算法的比较

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摘要

Lange and Carson (1984 J. Comput. Assist. Tomogr. 8 306-16) defined image reconstruction for transmission tomography as a maximum likelihood estimation problem and derived an expectation maximization (EM) algorithm to obtain the maximum likelihood image estimate. However, in the maximization step or M-step of the EM algorithm, an approximation is made in the solution which can affect the image quality, particularly in the case of domains with high attenuating material. O'Sullivan and Benac (2007 IEEE Trans. Med. Imaging 26 283-97) reformulated the maximum likelihood problem as a double minimization of an I-divergence to obtain a family of image reconstruction algorithms, called the alternating minimization (AM) algorithm. The AM algorithm increases the log-likelihood function while minimizing the I-divergence. In this work, we implement the AM algorithm for image reconstruction in gamma ray tomography for industrial applications. Experimental gamma ray transmission data obtained with a fan beam geometry gamma ray scanner, and simulated transmission data based on a synthetic phantom, with two phases (water and air) were considered in this study. Image reconstruction was carried out with these data using the AM and the EM algorithms to determine and quantitatively compare the holdup distribution images of the two phases in the phantoms. When compared to the EM algorithm, the AM algorithm shows qualitative and quantitative improvement in the holdup distribution images of the two phases for both the experimental and the simulated gamma ray transmission data.
机译：Lange和Carson（1984 J. Comput。Assist。Tomogr。8 306-16）将透射层析成像的图像重建定义为最大似然估计问题，并推导了期望最大化（EM）算法以获得最大似然图像估计。但是，在EM算法的最大化步骤或M步骤中，在解决方案中进行了近似估计，这可能会影响图像质量，特别是在具有高衰减材料的域的情况下。 O'Sullivan和Benac（2007 IEEE Trans。Med。Imaging 26 283-97）将I散度的两次最小化重新定义为最大似然问题，以获得一系列图像重建算法，称为交替最小化（AM）算法。 AM算法增加了对数似然函数，同时使I散度最小。在这项工作中，我们实现了用于工业应用的伽玛射线断层扫描中图像重建的AM算法。在这项研究中考虑了用扇形束几何伽马射线扫描仪获得的实验性伽马射线透射数据，以及基于合成体模的两相（水和空气）的模拟透射数据。使用AM和EM算法对这些数据进行图像重建，以确定并定量比较体模中两相的保持率分布图像。当与EM算法相比时，对于实验和模拟的伽马射线传输数据，AM算法在两相的滞留率分布图像中显示出定性和定量的改进。

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