# Enhancing Dynamic CT Image Reconstruction with Neural Fields and Optical Flow

arXiv: https://arxiv.org/abs/2406.01299 · HTML: https://mlsanity.com/paper/2406.01299/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 70 references that are in the map.
- First posted on arXiv 3 Jun 2024.

## Builds on (most cited first, 26 of 26)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks](https://mlsanity.com/paper/2012.10047/) (2020)
- [Dynamic CT Reconstruction from Limited Views with Implicit Neural Representations and Parametric Motion Fields](https://mlsanity.com/paper/2104.11745/) (2021)
- [Recovery of Continuous 3D Refractive Index Maps from Discrete Intensity-Only Measurements using Neural Fields](https://mlsanity.com/paper/2112.00002/) (2021)
- [Spatiotemporal implicit neural representation for unsupervised dynamic MRI reconstruction](https://mlsanity.com/paper/2301.00127/) (2022)
- [Neural Implicit k-Space for Binning-free Non-Cartesian Cardiac MR Imaging](https://mlsanity.com/paper/2212.08479/) (2022)
- [A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients](https://mlsanity.com/paper/1809.07321/) (2018)
- [Self-Supervised Coordinate Projection Network for Sparse-View Computed Tomography](https://mlsanity.com/paper/2209.05483/) (2022)
- [Going Off-Grid: Continuous Implicit Neural Representations for 3D Vascular Modeling](https://mlsanity.com/paper/2207.14663/) (2022)
- [Implicit Neural Networks with Fourier-Feature Inputs for Free-breathing Cardiac MRI Reconstruction](https://mlsanity.com/paper/2305.06822/) (2023)
- [WarpPINN: Cine-MR image registration with physics-informed neural networks](https://mlsanity.com/paper/2211.12549/) (2022)
- [Unsupervised reconstruction of accelerated cardiac cine MRI using Neural Fields](https://mlsanity.com/paper/2307.14363/) (2023)
- [Compressed Sensing Plus Motion (CS+M): A New Perspective for Improving Undersampled MR Image Reconstruction](https://mlsanity.com/paper/1810.10828/) (2018)
- [A Variational Model for Joint Motion Estimation and Image Reconstruction](https://mlsanity.com/paper/1607.03255/) (2016)
- [A Variational Reconstruction Method for Undersampled Dynamic X-ray Tomography based on Physical Motion Models](https://mlsanity.com/paper/1705.06079/) (2017)
- [Image reconstruction in dynamic inverse problems with temporal models](https://mlsanity.com/paper/2007.10238/) (2020)
- [A Memory-Efficient Dynamic Image Reconstruction Method using Neural Fields](https://mlsanity.com/paper/2205.05585/) (2022)
- [ProxNF: Neural Field Proximal Training for High-Resolution 4D Dynamic Image Reconstruction](https://mlsanity.com/paper/2403.03860/) (2024)
- [STEMPO -- dynamic X-ray tomography phantom](https://mlsanity.com/paper/2209.12471/) (2022)

## Built on by (most cited first, 1 of 1)

- [Towards Understanding the Benefits of Neural Network Parameterizations in Geophysical Inversions: A Study With Neural Fields](https://mlsanity.com/paper/2503.17503/) (2025)

## Abstract (arXiv)

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.