3D and 4D Phase Retrieval using Deep Learning


X-ray phase contrast imaging (PCI) is the most promising development of X-ray imaging techniques since their invention by Röntgen, allowing an increase in sensitivity of more than three orders of magnitude, and therefore potentially large decreases in imaging dose as well as strongly improved contrast in soft tissue without contrast agents. In order to exploit the phase information, a computational step is needed to reconstruct the phase, and possibly the attenuation, which is called phase retrieval. Phase retrieval is a non-linear ill-posed inverse problem. The development of deep learning methods in recent years has led to many advances in image and signal processing.

We have recently developed new non-linear methods for phase retrieval based on deep learning and transfer learning (training on simulated data). These include end-to-end methods, methods based on Generative Adversarial Networks (GAN) and algorithm unrolling methods, where parts of an iterative algorithm are replaced with neural networks and the iterations are learned, allowing to take into account the physics model of image formation while learning a regularization. These types of methods can reduce the calculation time by several orders of magnitude, while improving image quality and robustness of reconstructions. These algorithms have yielded exceptional initial results when applied to test objects.

Based on these results in propagation-based PCI (PBI), the aim of this project is to extend the developed algorithms to tomographic and 4D imaging in PBI, and to related phase contrast techniques. In this project, we will focus on high-frequency imaging (3D+t) using storage rings and X-ray Free Electron Laser (XFEL), Modulation-Based Imaging (MoBI) including dark-field imaging (DFI) (3D+scattering) and phase retrieval with Spectral Photon Counting Imaging (SPCI) and Computed Tomography (SPCCT) (3D+spectrum). The developed algorithms will be made available through the PyPhase package. The developed algorithms will be applied to imaging of animal models of osteoarthritis and osteoarthrosis. Faster reconstructions, higher image quality and more robust algorithms will improve diagnosis and analysis both in a clinical and pre-clinical setting. This work requires strong skills in inverse problems for the elaboration of the algorithms and their components, as well as expertise in the applications to bring them to routine use. To meet the challenges posed by the research project, we bring together an international team of imaging physicists, inverse problems specialists, algorithm specialists and biologists.


One PhD student has been hired on the subject "Image reconstruction in modulation-based and spectral X-ray phase contrast imaging using deep learning."

One postdoctoral fellow will be hired on the subject "3D and 4D phase retrieval in propagation-based X-ray phase contrast imaging using deep learning".


Langer M, Mom K, Sixou B, "Deep learning for phase retrieval from Fresnel diffraction patterns," 11th Applied Inverse Problems Conference, Göttingen, Germany, invited talk, 2023.

Published on  January 11, 2024
Updated on January 11, 2024