In x-ray multispectral (or photon-counting) computed tomography (MCT), the object of interest is scanned under multiple x-ray spectra, and it can acquire more information about the scanned object than conventional CT, in which only one x-ray spectrum is used. The obtained polychromatic projections are utilized to perform material-selective and energy-selective image reconstruction. Compared with the conventional single spectral CT, MCT has a superior material distinguishability. Therefore, it has wide potential applications in both medical and industrial areas. However, the nonlinearity and ill condition of the MCT problem make it difficult to get high-quality and fast convergence of images for existing MCT reconstruction algorithms. In this paper, we proposed an iterative reconstruction algorithm based on an oblique projection modification technique (OPMT) for fast basis material decomposition of MCT. In the case of geometric inconsistency, along the current x-ray path, the oblique projection modification direction not only relates to the polychromatic projection equation of the known spectrum, but it also comprehensively refers to the polychromatic projection equation information of the unknown spectra. Moreover, the ray-by-ray correction makes it applicable to geometrically consistent projection data. One feature of the proposed algorithm is its fast convergence speed. The OPMT considers the information from multiple polychromatic projection equations, which greatly speeds up the convergence of MCT reconstructed images. Another feature of the proposed algorithm is its high flexibility. The ray-by-ray correction will be suitable for any common MCT scanning mode. The proposed algorithm is validated with numerical experiments from both simulated and real data. Compared with the ASD-NC-POCS and E-ART algorithms, the proposed algorithm achieved high-quality reconstructed images while accelerating the convergence speed of them.

在 X 射线多光谱（或光子计数）计算机断层扫描 (MCT) 中，在多个 X 射线光谱下扫描感兴趣的对象，与传统 CT 相比，它可以获得更多关于被扫描对象的信息，其中只有一个 X-使用射线光谱。获得的多色投影用于执行材料选择性和能量选择性图像重建。与传统的单光谱CT相比，MCT具有优越的材料分辨能力。因此，它在医疗和工业领域都有广泛的潜在应用。然而，MCT问题的非线性和病态使得现有的MCT重建算法难以获得高质量和快速收敛的图像。在本文中，我们提出了一种基于斜投影修正技术 (OPMT) 的迭代重建算法，用于 MCT 的快速基材料分解。在几何不一致的情况下，沿当前X射线路径，斜投影修正方向不仅涉及已知光谱的多色投影方程，还综合涉及未知光谱的多色投影方程信息。此外，逐射线校正使其适用于几何一致的投影数据。所提出算法的一个特点是其收敛速度快。OPMT考虑了来自多个多色投影方程的信息，大大加快了MCT重建图像的收敛速度。所提出算法的另一个特点是它的高灵活性。逐射线校正将适用于任何常见的 MCT 扫描模式。所提出的算法通过模拟和真实数据的数值实验得到验证。与ASD-NC-POCS和E-ART算法相比，该算法在加快收敛速度​​的同时实现了高质量的重建图像。