  Machine learning methods for computational imaging require uncertainty
estimation to be reliable in real settings. While Bayesian models offer a
computationally tractable way of recovering uncertainty, they need large data
volumes to be trained, which in imaging applications implicates prohibitively
expensive collections with specific imaging instruments. This paper introduces
a novel framework to train variational inference for inverse problems
exploiting in combination few experimentally collected data, domain expertise
and existing image data sets. In such a way, Bayesian machine learning models
can solve imaging inverse problems with minimal data collection efforts.
Extensive simulated experiments show the advantages of the proposed framework.
The approach is then applied to two real experimental optics settings:
holographic image reconstruction and imaging through highly scattering media.
In both settings, state of the art reconstructions are achieved with little
collection of training data.
