  We present a tomographic imaging technique, termed Deep Prior Diffraction
Tomography (DP-DT), to reconstruct the 3D refractive index (RI) of thick
biological samples at high resolution from a sequence of low-resolution images
collected under angularly varying illumination. DP-DT processes the multi-angle
data using a phase retrieval algorithm that is extended by a deep image prior
(DIP), which reparameterizes the 3D sample reconstruction with an untrained,
deep generative 3D convolutional neural network (CNN). We show that DP-DT
effectively addresses the missing cone problem, which otherwise degrades the
resolution and quality of standard 3D reconstruction algorithms. As DP-DT does
not require pre-captured data or pre-training, it is not biased towards any
particular dataset. Hence, it is a general technique that can be applied to a
wide variety of 3D samples, including scenarios in which large datasets for
supervised training would be infeasible or expensive. We applied DP-DT to
obtain 3D RI maps of bead phantoms and complex biological specimens, both in
simulation and experiment, and show that DP-DT produces higher-quality results
than standard regularization techniques. We further demonstrate the generality
of DP-DT, using two different scattering models, the first Born and multi-slice
models. Our results point to the potential benefits of DP-DT for other 3D
imaging modalities, including X-ray computed tomography, magnetic resonance
imaging, and electron microscopy.
