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.
View on arXiv