Learned image reconstruction techniques using deep neural networks have recently gained popularity, and have delivered promising empirical results. However, most approaches focus on one single recovery for each observation, and thus neglect the uncertainty information. In this work, we develop a novel computational framework that approximates the posterior distribution of the unknown image at each query observation. The proposed framework is very flexible: It handles implicit noise models and priors, it incorporates the data formation process (i.e., the forward operator), and the learned reconstructive properties are transferable between different datasets. Once the network is trained using the conditional variational autoencoder loss, it provides a computationally efficient sampler for the approximate posterior distribution via feed-forward propagation, and the summarizing statistics of the generated samples are used for both point-estimation and uncertainty quantification. We illustrate the proposed framework with extensive numerical experiments on positron emission tomography (with both moderate and low count levels) showing that the framework generates high-quality samples when compared with state-of-the-art methods.
翻译:利用深神经网络进行图像重建的学习技术最近越来越受欢迎,并取得了有希望的经验结果。然而,大多数方法侧重于对每个观测进行单一的恢复,从而忽视了不确定信息。在这项工作中,我们开发了一个新的计算框架,在每次查询观测中,与未知图像的后方分布相近。拟议框架非常灵活:它处理隐含噪音模型和前方,它包含数据形成过程(即前方操作员),而所学的重建特性在不同数据集之间可转让。一旦利用有条件的变异自动coder损失对网络进行了培训,它就为通过饲料向前传播的近似后方分布提供了一种计算效率高的取样器,所生成样本的汇总统计数据被用于点估和不确定性的量化。我们用大量数字实验来说明拟议框架,对活性摄影(中值和低值水平)进行了广泛的数字实验,表明与最新方法相比,框架会产生高质量的样本。