ProtonVDA LLC, Naperville, Illinois, USA.
Moscow State University, Moscow, Russian Federation.
J Appl Clin Med Phys. 2023 Sep;24(9):e14114. doi: 10.1002/acm2.14114. Epub 2023 Aug 13.
Whereas filtered back projection algorithms for voxel-based CT image reconstruction have noise properties defined by the filter, iterative algorithms must stop at some point in their convergence and do not necessarily produce consistent noise properties for images with different degrees of heterogeneity.
A least-squares iterative algorithm for proton CT (pCT) image reconstruction converges toward a unique solution for relative stopping power (RSP) that optimally fits the protons. We present a stopping criterion that delivers solutions with the property that correlations of RSP noise between voxels are relatively low. This provides a method to produce pCT images with consistent noise properties useful for proton therapy treatment planning, which relies on summing RSP along lines of voxels. Consistent noise properties will also be useful for future studies of image quality using metrics such as contrast to noise ratio, and to compare RSP noise and dose of pCT with other modalities such as dual-energy CT.
With simulated and real images with varying heterogeneity from a prototype clinical proton imaging system, we calculate average RSP correlations between voxel pairs in uniform regions-of-interest versus distance between voxels. We define a parameter r, the remaining distance to the unique solution relative to estimated RSP noise, and our stopping criterion is based on r falling below a chosen value.
We find large correlations between voxels for larger values of r, and anticorrelations for smaller values. For r in the range of 0.5-1, voxels are relatively uncorrelated, and compared to smaller values of r have lower noise with only slight loss of spatial resolution.
Iterative algorithms not using a specific metric or rationale for stopping iterations may produce images with an unknown and arbitrary level of convergence or smoothing. We resolve this issue by stopping iterations of a least-squares iterative algorithm when r reaches the range of 0.5-1. This defines a pCT image reconstruction method with consistent statistical properties optimal for clinical use, including for treatment planning with pCT images.
基于体素的 CT 图像重建的滤波反投影算法的噪声特性由滤波器定义，而迭代算法必须在其收敛的某个点停止，并且对于不同异质性程度的图像不一定产生一致的噪声特性。
我们提出了一种用于质子 CT（pCT）图像重建的最小二乘迭代算法，对于与质子最佳拟合的相对停止功率（RSP），该算法收敛到唯一的解。我们提出了一个停止准则，该准则提供了一种方法，该方法产生的RSP 噪声在体素之间相关性相对较低的解。这为质子治疗计划提供了具有一致噪声特性的 pCT 图像生成方法，该方法依赖于沿体素线求和 RSP。一致的噪声特性对于使用对比度噪声比等指标进行图像质量的未来研究以及将 pCT 的 RSP 噪声和剂量与双能 CT 等其他模态进行比较也将非常有用。
我们使用来自原型临床质子成像系统的具有不同异质性的模拟和真实图像，计算均匀感兴趣区域中体素对之间的平均 RSP 相关性与体素之间的距离。我们定义了一个参数 r，即相对于估计的 RSP 噪声，到唯一解的剩余距离，我们的停止准则基于 r 低于选定值。
我们发现 r 较大时体素之间存在较大的相关性，而 r 较小时存在反相关性。对于 r 在 0.5-1 的范围内，体素相对不相关，与 r 较小的情况相比，噪声较低，空间分辨率仅略有降低。
不使用特定度量标准或停止迭代的基本原理的迭代算法可能会产生未知和任意收敛或平滑程度的图像。我们通过在 r 达到 0.5-1 的范围内时停止最小二乘迭代算法的迭代来解决此问题。这定义了一种具有一致统计特性的 pCT 图像重建方法，最适合临床使用，包括使用 pCT 图像进行治疗计划。
