Shi Hongli, Yang Zhi, Luo Shuqian
J Xray Sci Technol. 2017;25(3):417-428. doi: 10.3233/XST-16187.
The beam hardening artifact is one of most important modalities of metal artifact for polychromatic X-ray computed tomography (CT), which can impair the image quality seriously.
An iterative approach is proposed to reduce beam hardening artifact caused by metallic components in polychromatic X-ray CT.
According to Lambert-Beer law, the (detected) projections can be expressed as monotonic nonlinear functions of element geometry projections, which are the theoretical projections produced only by the pixel intensities (image grayscale) of certain element (component). With help of a prior knowledge on spectrum distribution of X-ray beam source and energy-dependent attenuation coefficients, the functions have explicit expressions. Newton-Raphson algorithm is employed to solve the functions. The solutions are named as the synthetical geometry projections, which are the nearly linear weighted sum of element geometry projections with respect to mean of each attenuation coefficient. In this process, the attenuation coefficients are modified to make Newton-Raphson iterative functions satisfy the convergence conditions of fixed pointed iteration(FPI) so that the solutions will approach the true synthetical geometry projections stably. The underlying images are obtained using the projections by general reconstruction algorithms such as the filtered back projection (FBP). The image gray values are adjusted according to the attenuation coefficient means to obtain proper CT numbers.
Several examples demonstrate the proposed approach is efficient in reducing beam hardening artifacts and has satisfactory performance in the term of some general criteria. In a simulation example, the normalized root mean square difference (NRMSD) can be reduced 17.52% compared to a newest algorithm.
Since the element geometry projections are free from the effect of beam hardening, the nearly linear weighted sum of them, the synthetical geometry projections, are almost free from the effect of beam hardening. By working out the synthetical geometry projections, the proposed approach becomes quite efficient in reducing beam hardening artifacts.
在多色X射线计算机断层扫描（CT）中，束硬化伪影是金属伪影的最重要形式之一，它会严重损害图像质量。
提出一种迭代方法以减少多色X射线CT中由金属部件引起的束硬化伪影。
根据朗伯-比尔定律，（检测到的）投影可表示为元素几何投影的单调非线性函数，元素几何投影是仅由特定元素（部件）的像素强度（图像灰度）产生的理论投影。借助X射线束源的光谱分布和能量依赖衰减系数的先验知识，这些函数具有明确的表达式。采用牛顿-拉夫逊算法求解这些函数。这些解被称为综合几何投影，它们是元素几何投影相对于每个衰减系数均值的近似线性加权和。在此过程中，对衰减系数进行修改，以使牛顿-拉夫逊迭代函数满足定点迭代（FPI）的收敛条件，从而使解稳定地接近真实综合几何投影。使用诸如滤波反投影（FBP）等通用重建算法通过投影获得基础图像。根据衰减系数均值调整图像灰度值以获得合适的CT值。
几个例子表明，所提出的方法在减少束硬化伪影方面是有效的，并且在一些通用标准方面具有令人满意的性能。在一个模拟例子中，与一种最新算法相比，归一化均方根差（NRMSD）可降低17.52%。
由于元素几何投影不受束硬化的影响，它们的近似线性加权和，即综合几何投影，几乎不受束硬化的影响。通过求解综合几何投影，所提出的方法在减少束硬化伪影方面变得非常有效。
