  Image reconstruction for dynamic inverse problems with highly undersampled
data poses a major challenge: not accounting for the dynamics of the process
leads to a non-realistic motion with no time regularity. Variational approaches
that penalize time derivatives or introduce motion model regularizers have been
proposed to relate subsequent frames and improve image quality using grid-based
discretization. Neural fields offer an alternative parametrization of the
desired spatiotemporal quantity with a deep neural network, a lightweight,
continuous, and biased towards smoothness representation. The inductive bias
has been exploited to enforce time regularity for dynamic inverse problems
resulting in neural fields optimized by minimizing a data-fidelity term only.
In this paper we investigate and show the benefits of introducing explicit
PDE-based motion regularizers, namely, the optical flow equation, in 2D+time
computed tomography for the optimization of neural fields. We also compare
neural fields against a grid-based solver and show that the former outperforms
the latter.
