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.

计算成像在确定稀疏测量中的隐藏信息方面起着重要的作用。我们提出了一种深度变分框架，利用深度生成模型来学习近似后验分布，以有效量化图像重建的不确定性，无需训练数据。我们通过使用基于流的模型参数化目标后验并最小化它们的 KL 散度来实现准确的不确定性估计。我们还引入了具有双向正则化的强大流模型，以增强稳定性，并通过梯度增强来增强表达能力。此外，我们还通过填充设计方法在潜在先验空间和目标后验空间实现了显著的方差减少。我们在几个基准任务和两个真实世界应用（即快速 MRI 和黑洞图像重建）上验证了我们的方法。我们的结果表明，我们的方法能够提供可靠且高质量的图像重建以及强大的不确定性估计。