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

TL;DR

This work tackles the ill-posed problem of reconstructing 4D X-ray dynamics from ultra-sparse spatiotemporal data by introducing 4D-PIONIX, a physics-informed neural implicit reconstruction that couples a 4D generator with GAN and a PDE-based loss derived from the full Navier–Stokes–Cahn–Hilliard physics. By training on simulated XMPI data of 4D droplet collisions and enforcing both data-consistency and physical constraints, 4D-PIONIX can recover reliable 4D dynamics from a single experiment and even predict unseen time points, performing comparably to multi-experiment baselines. The approach outperforms 4D-ONIX in scenarios with ultra-sparse data by leveraging the full physical model to constrain the reconstruction, reducing data requirements while enabling temporal super-resolution. These results suggest broad applicability to time-resolved tomography and other sparse XMPI-like modalities, with potential to also infer unknown physical parameters in rapid 4D processes.

Abstract

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.

Figures (4)

• Figure 1: Conceptual configuration of time-resolved X-ray tomography and XMPI. (a) Time-resolved X-ray tomography requires continuous rotation of the sample to acquire projection images from different angles over time; (b) XMPI is a rotation-free technique that generates multiple secondary X-ray beams that illuminate the sample from different angles simultaneously. This figure is adapted from Ref. zhang2024phd.
• Figure 2: Examples of simulated 3D objects and projection images at eight different time points. The first row shows the simulated 3D object. The second and the third rows show the simulated 2D projection images at $\varphi_1 = \ang{0}$ and $\varphi_2 = \ang{23.8}$, respectively.
• Figure 3: (a) Overview of the 4D-PIONIX workflow. The 4D representation generates the mapping from the 4D spatial-temporal coordinates (x,t) to the physical properties of the sample. The representation is constrained by i) self-consistency between the generated and recorded projections at given angles, ii) the PDE provided by the full physical model, and iii) feedback from the discriminator based on the generated projections at random angles. (b) Generation of the projection images. For each ray directed at a given projection angle, we integrate the refractive index along the ray using the principles of X-ray propagation and interaction with matter. The projection image is formed after sampling all the rays that generate a detector image. This figure is adapted from Ref. zhang20244d.
• Figure 4: Reconstruction results. (a) Ground truths (1) and reconstructions using 4D-PIONIX, 15-frame dataset (2); 4D-PIONIX, 75-frame dataset (3); 4D-ONIX, 1-experiment dataset (4); 4D-ONIX, 16-experiment dataset (5) at eight time points. At the time points marked in red, projection images are unavailable in the 15-frame dataset, while projection images are available for all four datasets at the time points marked in black. (b)-(d) Comparison of the distribution as a function of time of 3D MSE (b), 3D DSSIM (c), and 3D resolution estimated by FSC analysis (d) under all four reconstruction settings.