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.

用于动态逆问题的图像重建：高度欠采样数据的图像重建是一个重大挑战，现有的变分方法和神经场方法被应用于改善图像质量并引入时间正则化，本文研究并展示了在 2D + 时间计算机断层扫描中引入显式的基于偏微分方程的运动正则化的好处，并比较了神经场与基于网格求解器的性能差异。