Liu Xiaofeng, Marin Thibault, Amal Tiss, Woo Jonghye, El Fakhri Georges, Ouyang Jinsong
Gordon Center for Medical Imaging, Radiology Department, Massachusetts General Hospital, Boston, MA 02114, USA.
Radiology Department, Harvard Medical School, Boston, MA 02115, USA.
ArXiv. 2023 Mar 17:arXiv:2303.10057v1.
In medical imaging, images are usually treated as deterministic, while their uncertainties are largely underexplored.
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.
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.
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.
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.
在医学成像中，图像通常被视为确定性的，而其不确定性在很大程度上未得到充分探索。
这项工作旨在利用深度学习有效地估计成像参数的后验分布，进而可用于推导最可能的参数及其不确定性。
我们基于深度学习的方法基于变分贝叶斯推理框架，该框架使用基于条件变分自编码器（CVAE）的两种不同深度神经网络实现，即CVAE-双编码器和CVAE-双解码器。传统的CVAE框架，即普通CVAE，可被视为这两种神经网络的简化情况。我们将这些方法应用于使用基于参考区域的动力学模型的动态脑PET成像模拟研究。
在模拟研究中，我们在给定时间-活度曲线测量值的情况下估计了PET动力学参数的后验分布。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罗（MCMC）采样的渐近无偏后验分布高度一致。普通CVAE也可用于估计后验分布，尽管其性能不如CVAE-双编码器和CVAE-双解码器。
我们评估了基于深度学习的方法在动态脑PET中估计后验分布的性能。我们的深度学习方法产生的后验分布与MCMC估计的无偏分布高度一致。所有这些神经网络都有不同的特点，用户可根据具体应用进行选择。所提出的方法具有通用性，可适用于其他问题。
