Radiological Physics Division, The Russell H. Morgan Department of Radiology and Radiological Science, Johns Hopkins University School of Medicine, 601 North Caroline Street, JHOC 4253, Baltimore, MD, 21287, USA.
Med Phys. 2020 Jun;47(5):2085-2098. doi: 10.1002/mp.14047. Epub 2020 Mar 24.
Smaller pixel sizes of x-ray photon counting detectors (PCDs) are advantageous for count rate capabilities but disadvantageous for charge sharing. With charge sharing, the energy of an x-ray photon may be split and one photon may produce two or more counts at adjacent pixels, both at lower energies than the incident energy. This "double-counting" increases noise variance and degrades the spectral response. Overall, it has a significantly negative impact on the performance of PCD-based computed tomography (CT). Charge sharing is induced by the detection physics and occurs regardless of count rates; thus, it is impossible to avoid. We propose in this paper a method that has a potential to address both noise and bias added by charge sharing.
We propose applying a multi-energy inter-pixel coincidence counter (MEICC) technique, which uses energy-dependent coincidence counters, keeps the book of charge sharing events during data acquisition, and provides the exact number of charge sharing occurrences, which can be used to either correct or compensate for them after the acquisition is completed. MEICC does not interfere with the primary counting process; therefore, PCDs with MEICC will remain as fast as those without MEICC. MEICC can be implemented using current electronics technology because its inter-pixel coincidence counters used to handle digital data are rather simple. We evaluated Cramér-Rao lower bound (CRLB) of PCDs with and without MEICC using a Monte Carlo simulation.
When the number of energy windows was four or larger and eight neighboring pixels were used, the CRLBs of 225-µm PCD with MEICC normalized by those of the current PCD with the same number of windows were 0.361-0.383 for water density images of two basis functions, which was only 5.7-16.4% worse than those of a PCD without charge sharing (which were at 0.329-0.358). In contrast, the normalized CRLBs of the PCD with one coincidence counter were 0.466-0.499, which were 37.3-45.6% worse than the PCD without charge sharing. The use of eight neighboring pixels provided ~10% better CRLB values than four neighboring pixels for MEICC. With four energy windows, decreasing the number of coincidence counters from 16 to 9 only slightly increased the CRLB from 0.255 to 0.269 (which corresponded to as little as a 5.5% change). The normalized CRLBs of MEICC for K-edge imaging (gold) were 0.295-0.426, while those of the one coincidence counter were 0.926-0.959 and the ideal PCDs were 0.126-0.146.
The proposed MEICC provides spectral information that can be used to address charge sharing problems in PCDs and is expected to satisfy the requirements for clinical x-ray CT. MEICC is very effective, especially for K-edge imaging, which requires accurate spectral information.
X 射线光子计数探测器（PCD）的较小像素尺寸有利于计数率性能，但不利于电荷共享。在电荷共享的情况下，一个 X 射线光子的能量可能会被分割，一个光子可能会在相邻的像素上产生两个或更多的计数，其能量都低于入射能量。这种“双重计数”会增加噪声方差，并降低光谱响应。总的来说，它对基于 PCD 的计算机断层扫描（CT）的性能有显著的负面影响。电荷共享是由检测物理学引起的，并且无论计数率如何都会发生；因此，无法避免。本文提出了一种方法，该方法有可能解决电荷共享引起的噪声和偏差。
我们提出应用一种多能量像素间符合计数器（MEICC）技术，该技术使用能量相关的符合计数器，在数据采集过程中保留电荷共享事件的记录，并提供确切的电荷共享发生次数，可在采集完成后用于校正或补偿。MEICC 不会干扰主要的计数过程；因此，具有 MEICC 的 PCD 将与没有 MEICC 的 PCD 一样快。MEICC 可以使用当前的电子技术来实现，因为用于处理数字数据的像素间符合计数器相对简单。我们使用蒙特卡罗模拟评估了具有和不具有 MEICC 的 PCD 的克劳厄-劳不等式下限（CRLB）。
当能量窗口数为四或更多且使用八个相邻像素时，具有 MEICC 的 225-µm PCD 的 CRLB 相对于具有相同数量窗口的当前 PCD 的归一化值为 0.361-0.383，这对于两种基函数的水密度图像，仅比没有电荷共享的 PCD（在 0.329-0.358 之间）差 5.7-16.4%。相比之下，具有一个符合计数器的 PCD 的归一化 CRLB 为 0.466-0.499，比没有电荷共享的 PCD 差 37.3-45.6%。使用八个相邻像素比使用四个相邻像素提供了约 10%更好的 CRLB 值。对于 MEICC，使用四个能量窗口时，将符合计数器的数量从 16 减少到 9 仅将 CRLB 从 0.255 略微增加到 0.269（仅对应于 5.5%的变化）。MEICC 的 K 边成像（金）的归一化 CRLB 为 0.295-0.426，而一个符合计数器的为 0.926-0.959，理想的 PCD 为 0.126-0.146。
所提出的 MEICC 提供了可用于解决 PCD 中电荷共享问题的光谱信息，有望满足临床 X 射线 CT 的要求。MEICC 非常有效，特别是对于需要准确光谱信息的 K 边成像。
