IEEE Trans Biomed Eng. 2021 Sep;68(9):2678-2688. doi: 10.1109/TBME.2020.3048661. Epub 2021 Aug 19.
The conditioning (well-posedness) of basis materials (functions) and spectral channelization play important roles in determining the performance of spectral imaging (material specific imaging and virtual monochromatic imaging/analysis) in photon-counting CT. Aimed at further understanding the fundamentals of photon-counting spectral CT and providing guidelines on its design and implementation, we propose a singular value decomposition (SVD) and analysis based approach in this work to assess the conditioning of spectral channelization and its impact on the performance of spectral imaging under both ideal and realistic detector spectral response.
Via simulation studies, in which the geometry of photon-counting CT is similar to a clinical CT, the condition number acquired via SVD and analysis is employed to assess the conditioning of spectral channelization in photon-counting CT and its impact on the performance of spectral imaging. The simulation study runs over two- and three-material decom-position based spectral imaging (material specific imaging and virtual monochromatic imaging/analysis over the energy range [18] [150] keV). Under both ideal and realistic detector spectral response, a specially designed phantom that mimics the soft and bony tissues in the head is utilized to quantitatively reveal the relationship between the conditioning (condition number) of spectral channelization and the performance (mainly noise and contrast-to-noise ratio) of spectral imaging in photon-counting CT. The simulation study is also extended over the cases wherein up to 50% spectral overlapping occurs.
The results show that, under ideal detector spectral response, the condition number of spectral channelization reaches the minimum while no overlapping occurs in spectral channels. The condition number of spectral channelization increments with increasing spectral overlapping in the channels. The distortion in detector's spectral response induced by scattering, charge-sharing and fluorescent escaping results in spectral overlapping in spectral channels and thus degrades the conditioning (larger condition number) of spectral channelization. Respectively, the noise increases and contrast-to-noise ratio decreases in material- specific imaging and virtual monochromatic imaging/analysis, while the condition number of spectral channelization increments with increasing spectral overlapping.
The SVD and analysis based approach can be utilized to systematically analyze the conditioning of spectral channelization and its impact on the performance of spectral imaging in photon-counting CT.
The approach proposed by us brings innovation and has significance. In addition to providing information for insightful understanding of the fundamentals, the approach proposed in this study and the data obtained so far may provide guidelines on the implementation of spectral imaging in photon-counting CT and energy-integration CT as well, along with its applicability to other x-ray related imaging modalities such as radiography and tomosynthesis.
在光子计数 CT 中，基材料（函数）的条件（适定性）和光谱通道化起着重要作用，决定了光谱成象（物质特异性成象和虚拟单色谱成象/分析）的性能。为了进一步了解光子计数光谱 CT 的基本原理，并为其设计和实现提供指导，我们在这项工作中提出了一种基于奇异值分解（SVD）和分析的方法，以评估光谱通道化的条件及其对理想和现实探测器光谱响应下光谱成象性能的影响。
通过模拟研究，其中光子计数 CT 的几何形状类似于临床 CT，通过 SVD 和分析获得的条件数用于评估光子计数 CT 中光谱通道化的条件及其对光谱成象性能的影响。模拟研究跨越了两种和三种材料分解的光谱成象（在能量范围[18]至[150]keV 内的物质特异性成象和虚拟单色谱成象/分析）。在理想和现实的探测器光谱响应下，利用一个特别设计的模拟头颈部软组织和骨组织的体模，定量揭示了光谱通道化的条件（条件数）与光子计数 CT 中光谱成象性能（主要是噪声和对比噪声比）之间的关系。模拟研究还扩展到光谱通道中存在高达 50%光谱重叠的情况。
结果表明，在理想的探测器光谱响应下，当光谱通道中没有重叠时，光谱通道化的条件数达到最小值。随着通道中光谱重叠的增加，光谱通道化的条件数增加。散射、电荷共享和荧光逃逸引起的探测器光谱响应的失真导致光谱通道中的光谱重叠，从而降低了光谱通道化的条件（更大的条件数）。相应地，在物质特异性成象和虚拟单色谱成象/分析中，噪声增加，对比噪声比降低，而光谱通道化的条件数随着光谱重叠的增加而增加。
基于 SVD 和分析的方法可用于系统地分析光子计数 CT 中光谱通道化的条件及其对光谱成象性能的影响。
我们提出的方法具有创新性和意义。除了为深入了解基本原理提供信息外，本研究提出的方法和迄今为止获得的数据还可为光子计数 CT 中光谱成象以及能量积分 CT 的实施提供指导，以及为其他与 X 射线相关的成象方式（如射线照相术和断层合成术）提供指导。
