  Computational image reconstruction algorithms generally produce a single
image without any measure of uncertainty or confidence. Regularized Maximum
Likelihood (RML) and feed-forward deep learning approaches for inverse problems
typically focus on recovering a point estimate. This is a serious limitation
when working with underdetermined imaging systems, where it is conceivable that
multiple image modes would be consistent with the measured data. Characterizing
the space of probable images that explain the observational data is therefore
crucial. In this paper, we propose a variational deep probabilistic imaging
approach to quantify reconstruction uncertainty. Deep Probabilistic Imaging
(DPI) employs an untrained deep generative model to estimate a posterior
distribution of an unobserved image. This approach does not require any
training data; instead, it optimizes the weights of a neural network to
generate image samples that fit a particular measurement dataset. Once the
network weights have been learned, the posterior distribution can be
efficiently sampled. We demonstrate this approach in the context of
interferometric radio imaging, which is used for black hole imaging with the
Event Horizon Telescope, and compressed sensing Magnetic Resonance Imaging
(MRI).
