  X-ray tomography is capable of imaging the interior of objects in three
dimensions non-invasively, with applications in biomedical imaging, materials
science, electronic inspection, and other fields. The reconstruction process
can be an ill-conditioned inverse problem, requiring regularization to obtain
satisfactory results. Recently, deep learning has been adopted for tomographic
reconstruction. Unlike iterative algorithms which require a distribution that
is known a priori, deep reconstruction networks can learn a prior distribution
through sampling the training distributions. In this work, we develop a
Physics-assisted Generative Adversarial Network (PGAN), a two-step algorithm
for tomographic reconstruction. In contrast to previous efforts, our PGAN
utilizes maximum-likelihood estimates derived from the measurements to
regularize the reconstruction with both known physics and the learned prior.
Compared with methods with less physics assisting in training, PGAN can reduce
the photon requirement with limited projection angles to achieve a given error
rate. The advantages of using a physics-assisted learned prior in X-ray
tomography may further enable low-photon nanoscale imaging.
