  Reconstructing dynamic, time-varying scenes with computed tomography (4D-CT)
is a challenging and ill-posed problem common to industrial and medical
settings. Existing 4D-CT reconstructions are designed for sparse sampling
schemes that require fast CT scanners to capture multiple, rapid revolutions
around the scene in order to generate high quality results. However, if the
scene is moving too fast, then the sampling occurs along a limited view and is
difficult to reconstruct due to spatiotemporal ambiguities. In this work, we
design a reconstruction pipeline using implicit neural representations coupled
with a novel parametric motion field warping to perform limited view 4D-CT
reconstruction of rapidly deforming scenes. Importantly, we utilize a
differentiable analysis-by-synthesis approach to compare with captured x-ray
sinogram data in a self-supervised fashion. Thus, our resulting optimization
method requires no training data to reconstruct the scene. We demonstrate that
our proposed system robustly reconstructs scenes containing deformable and
periodic motion and validate against state-of-the-art baselines. Further, we
demonstrate an ability to reconstruct continuous spatiotemporal representations
of our scenes and upsample them to arbitrary volumes and frame rates
post-optimization. This research opens a new avenue for implicit neural
representations in computed tomography reconstruction in general.
