  4D time-space reconstruction of dynamic events or deforming objects using
X-ray computed tomography (CT) is an extremely ill-posed inverse problem.
Existing approaches assume that the object remains static for the duration of
several tens or hundreds of X-ray projection measurement images (reconstruction
of consecutive limited-angle CT scans). However, this is an unrealistic
assumption for many in-situ experiments that causes spurious artifacts and
inaccurate morphological reconstructions of the object. To solve this problem,
we propose to perform a 4D time-space reconstruction using a distributed
implicit neural representation (DINR) network that is trained using a novel
distributed stochastic training algorithm. Our DINR network learns to
reconstruct the object at its output by iterative optimization of its network
parameters such that the measured projection images best match the output of
the CT forward measurement model. We use a continuous time and space forward
measurement model that is a function of the DINR outputs at a sparsely sampled
set of continuous valued object coordinates. Unlike existing state-of-the-art
neural representation architectures that forward and back propagate through
dense voxel grids that sample the object's entire time-space coordinates, we
only propagate through the DINR at a small subset of object coordinates in each
iteration resulting in an order-of-magnitude reduction in memory and compute
for training. DINR leverages distributed computation across several compute
nodes and GPUs to produce high-fidelity 4D time-space reconstructions even for
extremely large CT data sizes. We use both simulated parallel-beam and
experimental cone-beam X-ray CT datasets to demonstrate the superior
performance of our approach.
