Beam hardening in x-ray computed tomography (CT) is inevitable because of the polychromatic x-ray spectrum and energy-dependent attenuation coefficients of materials, leading to the underestimation of artifacts arising from projection data, especially on metal regions. State-of-the-art research on beam-hardening artifacts is based on a numerical method that recursively performs CT reconstruction, which leads to a heavy computational burden. To address this computational issue, we propose a constrained beam-hardening estimator that provides an efficient numerical solution via a linear combination of two images reconstructed only once during the entire process. The proposed estimator reflects the geometry of metal objects and physical characteristics of beam hardening during the transmission of polychromatic x-rays through a material. Most of the associated parameters are numerically obtained from an initial uncorrected CT image and forward projection transformation without additional optimization procedures. Only the unknown parameter related to beam-hardening artifacts is fine-tuned by linear optimization, which is performed only in the reconstruction image domain. The proposed approach was systematically assessed using numerical simulations and phantom data for qualitative and quantitative comparisons. Compared with existing sinogram inpainting-based and model-based approaches, the proposed scheme in conjunction with the constrained beam-hardening estimator not only provided improved image quality in areas surrounding the metal but also achieved fast beam-hardening correction owing to the analytical reconstruction structure. This work may have significant implications in improving dose calculation accuracy or target volume delineation for treatment planning in radiotherapy.

由于材料的多色 X 射线光谱和能量相关的衰减系数，X 射线计算机断层扫描 (CT) 中的光束硬化是不可避免的，导致低估投影数据产生的伪影，特别是在金属区域。对光束硬化伪影的最新研究是基于递归执行 CT 重建的数值方法，这会导致繁重的计算负担。为了解决这个计算问题，我们提出了一种受约束的光束硬化估计器，它通过在整个过程中仅重建一次的两个图像的线性组合来提供有效的数值解决方案。所提出的估计器反映了多色 X 射线通过材料传输期间金属物体的几何形状和光束硬化的物理特性。大多数相关参数是从初始未校正的 CT 图像和正投影变换以数值方式获得的，无需额外的优化程序。只有与光束硬化伪影相关的未知参数通过线性优化进行微调，这仅在重建图像域中执行。使用数值模拟和虚拟数据系统地评估了所提出的方法，以进行定性和定量比较。与现有的基于正弦图修复和基于模型的方法相比，所提出的方案与约束光束硬化估计器相结合，不仅提高了金属周围区域的图像质量，而且由于解析重建结构实现了快速的光束硬化校正。 .