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.

翻译：本文研究动态计算机断层扫描的图像重建问题。目标物体相对于测量采集速率的运动导致测量数据在时间维度高度解析但在空间维度高度欠采样。此类问题面临主要挑战：若不考虑过程的动态特性，将导致重建结果质量低下且运动失真。已有研究提出基于经典网格离散化的变分方法，通过惩罚时间演化来关联相邻帧并改善图像质量。神经场作为一种新兴方法，利用低维输入神经网络对感兴趣量进行参数化，具有轻量化、连续性和偏向平滑表示的优势。在求解动态逆问题时，已有研究仅通过最小化数据保真项来利用神经场的平滑特性。本文研究并展示了基于偏微分方程（即光流方程）引入显式运动正则化器对神经场优化的益处。我们将其与未正则化方法进行对比，证明了重建质量的提升。同时，我们将神经场与基于网格的求解器进行比较，结果表明在该任务中神经场在峰值信噪比指标上优于网格方法。