  Phase recovery from intensity-only measurements forms the heart of coherent
imaging techniques and holography. Here we demonstrate that a neural network
can learn to perform phase recovery and holographic image reconstruction after
appropriate training. This deep learning-based approach provides an entirely
new framework to conduct holographic imaging by rapidly eliminating twin-image
and self-interference related spatial artifacts. Compared to existing
approaches, this neural network based method is significantly faster to
compute, and reconstructs improved phase and amplitude images of the objects
using only one hologram, i.e., requires less number of measurements in addition
to being computationally faster. We validated this method by reconstructing
phase and amplitude images of various samples, including blood and Pap smears,
and tissue sections. These results are broadly applicable to any phase recovery
problem, and highlight that through machine learning challenging problems in
imaging science can be overcome, providing new avenues to design powerful
computational imaging systems.
