  We address the problem of reconstructing X-Ray tomographic images from scarce
measurements by interpolating missing acquisitions using a self-supervised
approach. To do so, we train shallow neural networks to combine two
neighbouring acquisitions into an estimated measurement at an intermediate
angle. This procedure yields an enhanced sequence of measurements that can be
reconstructed using standard methods, or further enhanced using regularisation
approaches.
  Unlike methods that improve the sequence of acquisitions using an initial
deterministic interpolation followed by machine-learning enhancement, we focus
on inferring one measurement at once. This allows the method to scale to 3D,
the computation to be faster and crucially, the interpolation to be
significantly better than the current methods, when they exist. We also
establish that a sequence of measurements must be processed as such, rather
than as an image or a volume. We do so by comparing interpolation and
up-sampling methods, and find that the latter significantly under-perform.
  We compare the performance of the proposed method against deterministic
interpolation and up-sampling procedures and find that it outperforms them,
even when used jointly with a state-of-the-art projection-data enhancement
approach using machine-learning. These results are obtained for 2D and 3D
imaging, on large biomedical datasets, in both projection space and image
space.
