背景:在医学成像中,图像通常被视为确定性的,虽然他们的不确定性在很大程度上没有得到充分的探索。
目的:这项工作旨在使用深度学习来有效估计成像参数的后验分布,这反过来又可以用来推导最可能的参数以及它们的不确定性。
方法:我们基于深度学习的方法基于变分贝叶斯推理框架,这是使用基于条件变分自动编码器(CVAE)的两个不同的深度神经网络实现的,CVAE-双编码器,和CVAE双解码器。传统的CVAE框架,也就是说,CVAE-香草,可以看作是这两个神经网络的简化案例。我们使用基于参考区域的动力学模型将这些方法应用于动态脑PET成像的模拟研究。
结果:在模拟研究中,我们估计了PET动力学参数的后验分布在时间-活动曲线的测量。我们提出的CVAE双编码器和CVAE双解码器产生的结果与马尔可夫链蒙特卡洛(MCMC)采样的渐近无偏后验分布非常吻合。CVAE-香草也可用于估计后验分布,尽管它的性能低于CVAE双编码器和CVAE双解码器。
结论:我们已经评估了深度学习方法在动态脑PET中估计后验分布的性能。我们的深度学习方法产生后验分布,这与MCMC估计的无偏分布非常吻合。所有这些神经网络都具有不同的特性,可以由用户选择用于特定应用。所提出的方法是通用的,可以适应其他问题。
BACKGROUND: In medical imaging, images are usually treated as deterministic, while their uncertainties are largely underexplored.
OBJECTIVE: 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, that is, 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 the 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.