Stretched sinograms for limited-angle tomographic reconstruction with
  neural networks
Kyle Luther Sebastian Seung
We present a direct method for limited angle tomographic reconstruction using
convolutional networks. The key to our method is to first stretch every tilt
view in the direction perpendicular to the tilt axis by the secant of the tilt
angle. These stretched views are then fed into a 2-D U-Net which directly
outputs the 3-D reconstruction. We train our networks by minimizing the mean
squared error between the network's generated reconstruction and a ground truth
3-D volume. To demonstrate and evaluate our method, we synthesize tilt views
from a 3-D image of fly brain tissue acquired with Focused Ion Beam Scanning
Electron Microscopy. We compare our method to using a U-Net to directly
reconstruct the unstretched tilt views and show that this simple stretching
procedure leads to significantly better reconstructions. We also compare to
using a network to clean up reconstructions generated by backprojection and
filtered backprojection, and find that this simple stretching procedure also
gives lower mean squared error on previously unseen images.