# Physics-informed 4D X-ray image reconstruction from ultra-sparse spatiotemporal data

arXiv: https://arxiv.org/abs/2504.03469 · HTML: https://mlsanity.com/paper/2504.03469/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 56 references that are in the map.
- First posted on arXiv 4 Apr 2025.

## Builds on (most cited first, 18 of 18)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Method](https://mlsanity.com/paper/2110.15832/) (2021)
- [Structure-Aware Sparse-View X-ray 3D Reconstruction](https://mlsanity.com/paper/2311.10959/) (2023)
- [MedNeRF: Medical Neural Radiance Fields for Reconstructing 3D-aware CT-Projections from a Single X-ray](https://mlsanity.com/paper/2202.01020/) (2022)
- [Physics Informed Neural Fields for Smoke Reconstruction with Sparse Data](https://mlsanity.com/paper/2206.06577/) (2022)
- [SAMP: Shape and Motion Priors for 4D Vehicle Reconstruction](https://mlsanity.com/paper/2005.00922/) (2020)
- [The DUNE Framework: Basic Concepts and Recent Developments](https://mlsanity.com/paper/1909.13672/) (2019)
- [Computed stereo lensless X-ray imaging](https://mlsanity.com/paper/1909.04520/) (2019)
- [Physics-Informed Learning for Time-Resolved Angiographic Contrast Agent Concentration Reconstruction](https://mlsanity.com/paper/2403.01993/) (2024)
- [Extendible and Efficient Python Framework for Solving Evolution Equations with Stabilized Discontinuous Galerkin Method](https://mlsanity.com/paper/2009.13416/) (2020)
- [ONIX: an X-ray deep-learning tool for 3D reconstructions from sparse views](https://mlsanity.com/paper/2203.00682/) (2022)
- [Megahertz X-ray Multi-projection imaging](https://mlsanity.com/paper/2305.11920/) (2023)
- [Development towards high-resolution kHz-speed rotation-free volumetric imaging](https://mlsanity.com/paper/2311.16149/) (2023)
- [4D-ONIX: A deep learning approach for reconstructing 3D movies from sparse X-ray projections](https://mlsanity.com/paper/2401.09508/) (2024)

## Abstract (arXiv)

The unprecedented X-ray flux density provided by modern X-ray sources offers new spatiotemporal possibilities for X-ray imaging of fast dynamic processes. Approaches to exploit such possibilities often result in either i) a limited number of projections or spatial information due to limited scanning speed, as in time-resolved tomography, or ii) a limited number of time points, as in stroboscopic imaging, making the reconstruction problem ill-posed and unlikely to be solved by classical reconstruction approaches. 4D reconstruction from such data requires sample priors, which can be included via deep learning (DL). State-of-the-art 4D reconstruction methods for X-ray imaging combine the power of AI and the physics of X-ray propagation to tackle the challenge of sparse views. However, most approaches do not constrain the physics of the studied process, i.e., a full physical model. Here we present 4D physics-informed optimized neural implicit X-ray imaging (4D-PIONIX), a novel physics-informed 4D X-ray image reconstruction method combining the full physical model and a state-of-the-art DL-based reconstruction method for 4D X-ray imaging from sparse views. We demonstrate and evaluate the potential of our approach by retrieving 4D information from ultra-sparse spatiotemporal acquisitions of simulated binary droplet collisions, a relevant fluid dynamic process. We envision that this work will open new spatiotemporal possibilities for various 4D X-ray imaging modalities, such as time-resolved X-ray tomography and more novel sparse acquisition approaches like X-ray multi-projection imaging, which will pave the way for investigations of various rapid 4D dynamics, such as fluid dynamics and composite testing.