Statistical characterization of the linear attenuation coefficient in polychromatic CT scans.
Statistical characterization of the linear attenuation coefficient in polychromatic CT scans.
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DOI：
10.1002/mp.14384
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发表时间：
2020-11
期刊：
影响因子：
3.8
通讯作者：
San José Estépar R
中科院分区：
文献类型：
--
作者：
Vegas G;San José Estépar R
提供一个统一的统计模型，该模型在对数变换后表征检测器处的集成x射线强度，并可扩展到重构图像中计算机断层扫描（CT）数字的表征。我们研究了探测器中多能x射线束的统计特性。首先，我们考虑通过描述其统计量的概率模型（复合泊松）来表征探测器处的集成x射线强度。分析了其性质，并解析导出了对数变换后的概率分布。最后，我们提出了一个更易于处理的概率分布，具有在表征中观察到的相同特征，即非中心伽玛（nc-Gamma）。这种分布在整个重建过程中表现出理想的统计特性。我们评估了整个蒙特卡罗模拟中统计模型推导中采用的假设，并通过西门子临床CT扫描中获得的水影和肺影验证了这些假设。我们使用95%置信水平的Kolmogorov-Smirnov检验的功率分析来评估理论分布和nc-Gamma之间的统计相似性。蒙特卡罗模拟得到的Kolmogorov-Smirnov拟合优度检验表明，对数积分后x射线强度的经验分布与nc-Gamma之间具有极高的一致性。用两个模型进行的实验验证证实了在所有情况下理论分布、提议的nc-Gamma和样本分布之间的良好匹配。我们推导了一个解析模型，描述了多色CT扫描传感器中线性衰减系数的后对数分布。我们还证明了nc-Gamma分布与理论分布很接近。这种分布也很好地近似于重建后的CT数，因为它自然地扩展了涉及滤波后投影重建的线性操作。这种概率模型可以为定义新的基于似然的多色扫描重建方法提供分析基础。
To provide a unifying statistical model that characterizes the integrated x-ray intensity at the detector after logarithmic transformation and can be extended to the characterization of computed tomography (CT) numbers in the reconstructed image. We study the statistical characteristics of polyenergetic x-ray beams in the detector. Firstly, we consider the characterization of the integrated x-ray intensity at the detector through a probabilistic model (compound Poisson) that describes its statistics. We analyze its properties and derive the probabilistic distribution after the logarithmic transformation analytically. Finally, we propose a more tractable probabilistic distribution with the same features observed in the characterization, the noncentral Gamma (nc-Gamma). This distribution exhibits desirable properties for the statistical characterization across the reconstruction process. We assess the assumptions adopted in the derivation of the statistical models throughout Monte Carlo simulations and validate them with a water phantom and a lung phantom acquired in a Siemens clinical CT scan. We evaluate the statistical similarities between the theoretical distribution and the nc-Gamma using a power analysis with a Kolmogorov-Smirnov test for a 95% confidence level. The Kolmogorov-Smirnov goodness-of-fit test obtained for the Monte Carlo simulation shows an extremely high agreement between the empirical distribution of the post-logarithmic-integrated x-ray intensity and the nc-Gamma. The experimental validation performed with both phantoms confirmed the excellent match between the theoretical distribution, the proposed nc-Gamma, and sample distributions in all situations. We derive an analytical model describing the post-log distribution of the linear attenuation coefficient in the sensor for polychromatic CT scans. We also demonstrate that the nc-Gamma distribution approximates well the theoretical distribution. This distribution also approximates well the CT numbers after reconstruction since it naturally extends across linear operations involved in filtered back projection reconstructions. This probabilistic model may provide the analytical foundation to define new likelihood-based reconstruction methodologies for polychromatic scans.
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DOI：
10.2217/iim.09.5
发表时间：
2009-10
期刊：
Imaging in medicine
影响因子：
--
作者：
Yu L;Liu X;Leng S;Kofler JM;Ramirez-Giraldo JC;Qu M;Christner J;Fletcher JG;McCollough CH
通讯作者：
McCollough CH
影响因子：
10.6
作者：
Erdogan, H;Fessler, JA
通讯作者：
Fessler, JA
影响因子：
10.9
作者：
Vegas-Sanchez-Ferrero, Gonzalo;Ledesma-Carbayo, Maria J.;San Jose Estepar, Raid
通讯作者：
San Jose Estepar, Raid
影响因子：
1
作者：
MOSCHOPOULOS, PG
通讯作者：
MOSCHOPOULOS, PG
影响因子：
3.8
作者：
Whiting, Bruce R.;Massoumzadeh, Parinaz;Williamson, Jeffrey F.
通讯作者：
Williamson, Jeffrey F.