Robust Generative Flows on Reliable Image Reconstruction without Training Data

Sirui Bi, Victor Fung, Jiaxin Zhang

Abstract: A key application of computational imaging is to determine the hidden information from a set of observed but sparse measurements. To fully characterize the uncertainty naturally induced by the sparse measurements, a robust inverse solver that is able to estimate the complete posterior of the unrecoverable targets is therefore important, with a potential to probabilistically interpret the observational data for decision making. In this work, we propose a deep variational framework that leverages a deep generative model to learn an approximate posterior distribution for quantifying image reconstruction uncertainty without training data. This is achieved by parameterizing the target posterior using a flow-based model and minimizing their KL divergence. To perform accurate uncertainty estimation, we propose a robust flow-based model where the stability is enhanced by adding bi-directional regularization and the expressivity is improved by using gradient boosting. We also found that the statistics of latent distribution are conservatively propagated to the posterior distribution through an invertible transformation and therefore introduce a space-filling design to achieve significant variance reduction on both latent prior space and target posterior space. We demonstrate our method on several benchmark tasks and two real-world applications (fastMRI and black hole image reconstruction) and show that it achieves a reliable and high-quality image reconstruction with robust uncertainty estimation.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics

Submission Guidelines: Yes

Please Choose The Closest Area That Your Submission Falls Into: Probabilistic Methods (eg, variational inference, causal inference, Gaussian processes)