Enhancing Dynamic CT Image Reconstruction with Neural Fields and Optical Flow

In this paper, we investigate image reconstruction for dynamic Computed Tomography. The motion of the target with respect to the measurement acquisition rate leads to highly resolved in time but highly undersampled in space measurements. Such problems pose a major challenge: not accounting for the dynamics of the process leads to a poor reconstruction with non-realistic motion. Variational approaches that penalize time evolution have been proposed to relate subsequent frames and improve image quality based on classical grid-based discretizations. Neural fields have emerged as a novel way to parameterize the quantity of interest using a neural network with a low-dimensional input, benefiting from being lightweight, continuous, and biased towards smooth representations. The latter property has been exploited when solving dynamic inverse problems with neural fields by minimizing a data-fidelity term only. We investigate and show the benefits of introducing explicit motion regularizers for dynamic inverse problems based on partial differential equations, namely, the optical flow equation, for the optimization of neural fields. We compare it against its unregularized counterpart and show the improvements in the reconstruction. We also compare neural fields against a grid-based solver and show that the former outperforms the latter in terms of PSNR in this task.