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

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. Four-dimensional (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 artificial intelligence 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, 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.