  In transmission X-ray microscopy (TXM) systems, the rotation of a scanned
sample might be restricted to a limited angular range to avoid collision to
other system parts or high attenuation at certain tilting angles. Image
reconstruction from such limited angle data suffers from artifacts due to
missing data. In this work, deep learning is applied to limited angle
reconstruction in TXMs for the first time. With the challenge to obtain
sufficient real data for training, training a deep neural network from
synthetic data is investigated. Particularly, the U-Net, the state-of-the-art
neural network in biomedical imaging, is trained from synthetic ellipsoid data
and multi-category data to reduce artifacts in filtered back-projection (FBP)
reconstruction images. The proposed method is evaluated on synthetic data and
real scanned chlorella data in $100^\circ$ limited angle tomography. For
synthetic test data, the U-Net significantly reduces root-mean-square error
(RMSE) from $2.55 \times 10^{-3}$ {\mu}m$^{-1}$ in the FBP reconstruction to
$1.21 \times 10^{-3}$ {\mu}m$^{-1}$ in the U-Net reconstruction, and also
improves structural similarity (SSIM) index from 0.625 to 0.920. With penalized
weighted least square denoising of measured projections, the RMSE and SSIM are
further improved to $1.16 \times 10^{-3}$ {\mu}m$^{-1}$ and 0.932,
respectively. For real test data, the proposed method remarkably improves the
3-D visualization of the subcellular structures in the chlorella cell, which
indicates its important value for nano-scale imaging in biology, nanoscience
and materials science.
