Exploring charge sharing compensation using inter-pixel coincidence counters for photon counting detectors by deep-learning from local information

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Photon counting detectors (PCDs) have well-acknowledged advantages in computed tomography (CT) imaging. However, charge sharing and other problems prevent PCDs from fully realizing the anticipated potential in diagnostic CT. PCDs with multi-energy inter-pixel coincidence counters (MEICC) have been proposed to provide particular information about charge sharing, thereby achieving lower Cramér-Rao Lower Bound (CRLB) than conventional PCDs when assessing its performance by estimating material thickness or virtual monochromatic attenuation integrals (VMAIs). This work explores charge sharing compensation using local spatial coincidence counter information for MEICC detectors through a deep-learning method.
Approach: By analyzing the impact of charge sharing on photon count detection, we designed our network with a focus on individual pixels. Employing MEICC data of patches centered on POIs as input, we utilized local information for effective charge sharing compensation. The output was VMAI at different energies to address real detector issues without knowledge of primary counts. To achieve data diversity, a fast and online data generation method was proposed to provide adequate training data. A new loss function was introduced to reduce bias for training with high-noise data. The proposed method was validated by Monte Carlo (MC) simulation data for MEICC detectors that were compared with conventional PCDs. 
Main-Results: For conventional data as a reference, networks trained on low-noise data yielded results with a minimal bias (about 0.7%) compared with > 3% for the polynomial fitting method. The results of networks trained on high-noise data exhibited a slightly increased bias (about 1.3%) but a significantly reduced standard deviation (STD) and normalized root mean square error (NRMSE). The simulation study of the MEICC detector demonstrated superior compared to the conventional detector across all the metrics. Specifically, for both networks trained on high-noise and low-noise data, their biases were reduced to about 1% and 0.6%, respectively. Meanwhile, the results from a MEICC detector were of about 10% lower noise than a conventional detector. Moreover, an ablation study showed that the additional loss function on bias was beneficial for training on high-noise data.
Significance: We demonstrated that a network-based method could utilize local information in PCDs effectively by patch-based learning to reduce the impact of charge sharing. MEICC detectors provide very valuable local spatial information by additional coincidence counters. Compared with MEICC detectors, conventional PCDs only have limited local spatial information for charge sharing compensation, resulting in higher bias and standard deviation in VMAI estimation with the same patch strategy.&#xD.