Integrated-type proton computed tomography (pCT) measures proton stopping power ratio (SPR) images for proton therapy treatment planning, but its image quality is degraded due to noise and scatter. Although several correction methods have been proposed, techniques that include estimation of uncertainty are limited. This study proposes a novel uncertainty-aware pCT image correction method using a Bayesian convolutional neural network (BCNN). A DenseNet-based BCNN was constructed to predict both a corrected SPR image and its uncertainty from a noisy SPR image. A total 432 noisy SPR images of 6 non-anthropomorphic and 3 head phantoms were collected with Monte Carlo simulations, while true noise-free images were calculated with known geometric and chemical components. Heteroscedastic loss and deep ensemble techniques were performed to estimate aleatoric and epistemic uncertainties by training 25 unique BCNN models. 200-epoch end-to-end training was performed for each model independently. Feasibility of the predicted uncertainty was demonstrated after applying two post-hoc calibrations and calculating spot-specific path length uncertainty distribution. For evaluation, accuracy of head SPR images and water-equivalent thickness (WET) corrected by the trained BCNN models was compared with a conventional method and non-Bayesian CNN model. BCNN-corrected SPR images represent noise-free images with high accuracy. Mean absolute error in test data was improved from 0.263 for uncorrected images to 0.0538 for BCNN-corrected images. Moreover, the calibrated uncertainty represents accurate confidence levels, and the BCNN-corrected calibrated WET was more accurate than non-Bayesian CNN with high statistical significance. Computation time for calculating one image and its uncertainties with 25 BCNN models is 0.7 s with a consumer grade GPU. Our model is able to predict accurate pCT images as well as two types of uncertainty. These uncertainties will be useful to identify potential cause of SPR errors and develop a spot-specific range margin criterion, toward elaboration of uncertainty-guided proton therapy.

集成式质子计算机断层扫描 (pCT) 测量质子停止能力比 (SPR) 图像用于质子治疗治疗计划，但其图像质量因噪声和散射而下降。尽管已经提出了几种校正方法，但包括不确定性估计的技术是有限的。本研究提出了一种使用贝叶斯卷积神经网络 (BCNN) 的新型不确定性感知 pCT 图像校正方法。构建了一个基于 DenseNet 的 BCNN 来预测校正后的 SPR 图像及其从嘈杂的 SPR 图像中的不确定性。蒙特卡罗模拟共收集了 6 个非拟人模型和 3 个头部模型的 432 个噪声 SPR 图像，而真正的无噪声图像是使用已知的几何和化学成分计算的。通过训练 25 个独特的 BCNN 模型，执行异方差损失和深度集成技术来估计任意和认知不确定性。对每个模型独立进行 200 次端到端训练。在应用两次事后校准并计算特定点的路径长度不确定性分布后，证明了预测不确定性的可行性。为了评估，将训练后的 BCNN 模型校正的头部 SPR 图像和水当量厚度 (WET) 的准确性与传统方法和非贝叶斯 CNN 模型进行了比较。BCNN 校正的 SPR 图像以高精度表示无噪声图像。测试数据的平均绝对误差从未校正图像的 0.263 提高到 BCNN 校正图像的 0.0538。此外，校准的不确定性代表准确的置信水平，并且 BCNN 校正的校准 WET 比非贝叶斯 CNN 更准确，具有较高的统计显着性。使用 25 个 BCNN 模型计算一张图像及其不确定性的计算时间为 0.7 秒，使用消费级 GPU。我们的模型能够预测准确的 pCT 图像以及两种类型的不确定性。这些不确定性将有助于识别 SPR 错误的潜在原因并制定特定点的范围裕度标准，以制定不确定性引导的质子治疗。