  The problem of phase retrieval, or the algorithmic recovery of lost phase
information from measured intensity alone, underlies various imaging methods
from astronomy to nanoscale imaging. Traditional methods of phase retrieval are
iterative in nature, and are therefore computationally expensive and time
consuming. More recently, deep learning (DL) models have been developed to
either provide learned priors to iterative phase retrieval or in some cases
completely replace phase retrieval with networks that learn to recover the lost
phase information from measured intensity alone. However, such models require
vast amounts of labeled data, which can only be obtained through simulation or
performing computationally prohibitive phase retrieval on hundreds of or even
thousands of experimental datasets. Using a 3D nanoscale X-ray imaging modality
(Bragg Coherent Diffraction Imaging or BCDI) as a representative technique, we
demonstrate AutoPhaseNN, a DL-based approach which learns to solve the phase
problem without labeled data. By incorporating the physics of the imaging
technique into the DL model during training, AutoPhaseNN learns to invert 3D
BCDI data from reciprocal space to real space in a single shot without ever
being shown real space images. Once trained, AutoPhaseNN is about one hundred
times faster than traditional iterative phase retrieval methods while providing
comparable image quality.
