  Deep learning has demonstrated superb efficacy in processing imaging data,
yet its suitability in solving challenging inverse problems in scientific
imaging has not been fully explored. Of immense interest is the determination
of local material properties from atomically-resolved imaging, such as electron
microscopy, where such information is encoded in subtle and complex data
signatures, and whose recovery and interpretation necessitate intensive
numerical simulations subject to the requirement of near-perfect knowledge of
the experimental setup. We demonstrate that an end-to-end deep learning model
can successfully recover 3-dimensional atomic distortions of a variety of oxide
perovskite materials from a single 2-dimensional experimental scanning
transmission electron (STEM) micrograph, in the process resolving a
longstanding question in the recovery of 3-D atomic distortions from STEM
experiments. Our results indicate that deep learning is a promising approach to
efficiently address unsolved inverse problems in scientific imaging and to
underpin novel material investigations at atomic resolution.
