X-ray computed tomography (CT) is a nondestructive imaging technique to reconstruct cross-sectional images of an object using x-ray measurements taken from different view angles for medical diagnosis, therapeutic planning, security screening, and other applications. In clinical practice, the x-ray tube emits polychromatic x-rays, and the x-ray detector array operates in the energy-integrating mode to acquire energy intensity. This physical process of x-ray imaging is accurately described by an energy-dependent non-linear integral equation on the basis of the Beer–Lambert law. However, the non-linear model is not invertible using a computationally efficient solution and is often approximated as a linear integral model in the form of the Radon transform, which basically loses energy-dependent information. This approximate model produces an inaccurate quantification of attenuation images, suffering from beam-hardening effects. In this paper, a machine learning-based approach is proposed to correct the model mismatch to achieve quantitative CT imaging. Specifically, a one-dimensional network model is proposed to learn a non-linear transform from a training dataset to map a polychromatic CT image to its monochromatic sinogram at a pre-specified energy level, realizing virtual monochromatic (VM) imaging effectively and efficiently. Our results show that the proposed method recovers high-quality monochromatic projections with an average relative error of less than 2%. The resultant x-ray VM imaging can be applied for beam-hardening correction, material differentiation and tissue characterization, and proton therapy treatment planning.

X 射线计算机断层扫描 (CT) 是一种非破坏性成像技术，可使用从不同视角获取的 X 射线测量值重建对象的横截面图像，用于医学诊断、治疗计划、安全筛查和其他应用。在临床实践中，X射线管发射多色X射线，X射线探测器阵列以能量积分模式工作以获取能量强度。这种 X 射线成像的物理过程可以通过基于 Beer-Lambert 定律的与能量相关的非线性积分方程准确描述。然而，非线性模型使用计算高效的解决方案不可逆，并且通常近似为 Radon 变换形式的线性积分模型，这基本上丢失了与能量相关的信息。这种近似模型会产生不准确的衰减图像量化，受到光束硬化效应的影响。在本文中，提出了一种基于机器学习的方法来校正模型失配以实现定量 CT 成像。具体而言，提出了一种一维网络模型来学习训练数据集的非线性变换，以将多色 CT 图像映射到预先指定能量水平的单色正弦图，有效且高效地实现虚拟单色 (VM) 成像。我们的结果表明，所提出的方法恢复了高质量的单色投影，平均相对误差小于 2%。由此产生的 X 射线 VM 成像可用于束硬化校正、材料区分和组织表征以及质子治疗治疗计划。