Spectral CT can separate basis materials, and thus it can provide information on material characterization and quantification. Such information can benefit various clinical applications. However, the presence of non-ideal effects in X-ray imaging systems limits the accuracy of basis images. To achieve high accuracy of material decomposition and high quality of basis images, a novel direct iterative basis material image reconstruction based on maximum a posteriori expectation–maximization algorithm (MAP-EM-DD) is proposed. Furthermore, by incorporating polar coordinate transformation into MAP-EM-DD, MAP-EM-PT-DD is proposed. The iterative formulas of MAP-EM-DD and MAP-EM-PT-DD are derived. To evaluate the proposed methods, a simulated cylinder phantom with inserts that contain polyethylene, hydroxyapatite, salt water, air, and aluminum is established. The methods are quantitatively evaluated for comparative studies. Results show that the proposed methods can remarkably reduce the noise of basis images and error of material decomposition and improve the contrast-to-noise ratios (CNRs) of each material-specific region. Compared with the image domain material decomposition based on FBP algorithm (FBP-IDD), MAP-EM-DD can reduce the noise levels of basis images ranging from 57.4 to 63.6% and the error levels of each material-specific region from 31.7 to 62.1%. Simultaneously, the CNRs of each material-specific region are improved ranging from 63.8 to 237.3%. Compared with MAP-EM-DD, MAP-EM-PT-DD can reduce the noise levels of basis images ranging from 21.4 to 23.6%, the error levels of each material-specific region ranging from 1.9 to 36.3%, and the reconstruction time of basis images by 14.1%.

中文翻译：

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基于MAP-EM算法的光谱CT直接迭代基础图像重建

光谱 CT 可以分离基础材料，因此它可以提供有关材料表征和量化的信息。这样的信息可以有益于各种临床应用。然而，X 射线成像系统中非理想效应的存在限制了基础图像的准确性。为了实现材料分解的高精度和高质量的基础图像，提出了一种基于最大后验期望最大化算法（MAP-EM-DD）的新型直接迭代基础材料图像重建。此外，通过将极坐标变换纳入 MAP-EM-DD，提出了 MAP-EM-PT-DD。推导出MAP-EM-DD和MAP-EM-PT-DD的迭代公式。为了评估所提出的方法，一个带有插入物的模拟圆柱体模型，其中包含聚乙烯、羟基磷灰石、盐水、空气、和铝成立。对这些方法进行定量评估以进行比较研究。结果表明，所提出的方法可以显着降低基础图像的噪声和材料分解的误差，并提高每个材料特定区域的对比度噪声比（CNR）。与基于FBP算法的图像域材料分解（FBP-IDD）相比，MAP-EM-DD可以将基础图像的噪声水平降低57.4%到63.6%，每个材料特定区域的误差水平从31.7%降低到62.1% %。同时，每个材料特定区域的 CNR 提高了 63.8% 到 237.3%。与 MAP-EM-DD 相比，MAP-EM-PT-DD 可以将基础图像的噪声水平降低 21.4% 到 23.6%，每个材料特定区域的误差水平从 1.9% 到 36.3%，