Background: In medical imaging, images are usually treated as deterministic, while their uncertainties are largely underexplored. Purpose: This work aims at using deep learning to efficiently estimate posterior distributions of imaging parameters, which in turn can be used to derive the most probable parameters as well as their uncertainties. Methods: Our deep learning-based approaches are based on a variational Bayesian inference framework, which is implemented using two different deep neural networks based on conditional variational auto-encoder (CVAE), CVAE-dual-encoder and CVAE-dual-decoder. The conventional CVAE framework, i.e., CVAE-vanilla, can be regarded as a simplified case of these two neural networks. We applied these approaches to a simulation study of dynamic brain PET imaging using a reference region-based kinetic model. Results: In the simulation study, we estimated posterior distributions of PET kinetic parameters given a measurement of time-activity curve. Our proposed CVAE-dual-encoder and CVAE-dual-decoder yield results that are in good agreement with the asymptotically unbiased posterior distributions sampled by Markov Chain Monte Carlo (MCMC). The CVAE-vanilla can also be used for estimating posterior distributions, although it has an inferior performance to both CVAE-dual-encoder and CVAE-dual-decoder. Conclusions: We have evaluated the performance of our deep learning approaches for estimating posterior distributions in dynamic brain PET. Our deep learning approaches yield posterior distributions, which are in good agreement with unbiased distributions estimated by MCMC. All these neural networks have different characteristics and can be chosen by the user for specific applications. The proposed methods are general and can be adapted to other problems.

翻译：背景：在医学成像中，图像通常被视为确定性结果，而其不确定性尚未得到充分探索。目的：本研究旨在利用深度学习高效估计成像参数的后验分布，从而推导出最可能参数值及其不确定性。方法：我们的深度学习方法基于变分贝叶斯推断框架，通过两种不同的深度神经网络实现：基于条件变分自编码器（CVAE）的CVAE-双编码器和CVAE-双解码器。传统CVAE框架（即CVAE-原始模型）可被视为这两种网络的简化形式。我们将这些方法应用于基于参考区域动力学模型的脑部动态PET仿真研究。结果：在仿真研究中，我们根据时间-活度曲线测量值估计了PET动力学参数的后验分布。所提出的CVAE-双编码器和CVAE-双解码器生成的结果与通过马尔可夫链蒙特卡洛（MCMC）采样的渐近无偏后验分布高度吻合。CVAE-原始模型也可用于估计后验分布，但其性能均次于CVAE-双编码器和CVAE-双解码器。结论：我们评估了深度学习方法在动态脑PET后验分布估计中的性能。深度学习方法生成的后验分布与MCMC估计的无偏分布高度一致。这些神经网络具有不同特性，用户可根据具体应用场景进行选择。所提出的方法具有通用性，可推广至其他研究问题。