Effect of errors in the system matrix on maximum a posteriori image reconstruction
Effect of errors in the system matrix on maximum a posteriori image reconstruction
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DOI：
10.1088/0031-9155/50/14/007
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发表时间：
2005-07-21
影响因子：
3.5
通讯作者：
Huesman, RH
中科院分区：
文献类型：
--
作者：
Qi, JY;Huesman, RH
基于统计的迭代图像重建方法已经被开发用于发射断层摄影。迭代图像重建中的一个重要组成部分是系统矩阵，它定义了从图像空间到数据空间的映射。几个小组已经证明，准确的系统矩阵可以提高单光子发射计算机断层扫描（SPECT）和正电子发射断层扫描（PET）的图像质量。虽然迭代方法适用于任意和复杂的系统模型，但真实的系统响应永远不会确切知道。在实践中，由于有限的计算和成像资源，还必须牺牲系统模型的准确性。本文分析了系统矩阵误差对基于最大后验原理的迭代图像重建方法的影响。我们推导出一个解析表达式，用于计算重建图像中的伪影，所述伪影是由使用一阶泰勒级数近似的系统矩阵中的误差引起的。该理论表达式用于确定发射层析成像中系统矩阵所需的最小精度。计算机模拟表明，理论结果在低噪声情况下工作得相当好。
Statistically based iterative image reconstruction methods have been developed for emission tomography. One important component in iterative image reconstruction is the system matrix, which defines the mapping from the image space to the data space. Several groups have demonstrated that an accurate system matrix can improve image quality in both single photon emission computed tomography (SPECT) and positron emission tomography (PET). While iterative methods are amenable to arbitrary and complicated system models, the true system response is never known exactly. In practice, one also has to sacrifice the accuracy of the system model because of limited computing and imaging resources. This paper analyses the effect of errors in the system matrix on iterative image reconstruction methods that are based on the maximum a posteriori principle. We derived an analytical expression for calculating artefacts in a reconstructed image that are caused by errors in the system matrix using the first-order Taylor series approximation. The theoretical expression is used to determine the required minimum accuracy of the system matrix in emission tomography. Computer simulations show that the theoretical results work reasonably well in low-noise situations.