On the Quantification of Image Reconstruction Uncertainty without
  Training Data
Sirui Bi Victor Fung Jiaxin Zhang
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.