Computational imaging plays a pivotal role in determining hidden information from sparse measurements. A robust inverse solver is crucial to fully characterize the uncertainty induced by these measurements, as it allows for the estimation of the complete posterior of unrecoverable targets. This, in turn, facilitates a probabilistic interpretation of observational data for decision-making. In this study, we propose a deep variational framework that leverages a deep generative model to learn an approximate posterior distribution to effectively quantify image reconstruction uncertainty without the need for training data. We parameterize the target posterior using a flow-based model and minimize their Kullback-Leibler (KL) divergence to achieve accurate uncertainty estimation. To bolster stability, we introduce a robust flow-based model with bi-directional regularization and enhance expressivity through gradient boosting. Additionally, we incorporate a space-filling design to achieve substantial variance reduction on both latent prior space and target posterior space. We validate our method on several benchmark tasks and two real-world applications, namely fastMRI and black hole image reconstruction. Our results indicate that our method provides reliable and high-quality image reconstruction with robust uncertainty estimation.

翻译：计算成像在从稀疏测量中确定隐藏信息方面发挥着关键作用。一个稳健的逆求解器对于全面表征这些测量所引发的不确定性至关重要，因为它能够估计不可恢复目标的完整后验分布，从而促进基于观测数据的概率性决策。本文提出一种深度变分框架，利用深度生成模型学习近似后验分布，在无需训练数据的情况下有效量化图像重建不确定性。我们采用基于流的模型参数化目标后验，并通过最小化其与真实后验的Kullback-Leibler散度来实现准确的不确定性估计。为增强稳定性，我们引入具有双向正则化的稳健流模型，并通过梯度提升提升模型表达能力。此外，我们采用空间填充设计以实现潜在先验空间和目标后验空间的方差显著降低。我们在多个基准任务及两个实际应用——快速MRI和黑洞图像重建——中验证了该方法。实验结果表明，我们的方法能够提供可靠且高质量的图像重建，并具备稳健的不确定性估计。