Learning neural representations for X-ray ptychography reconstruction with unknown probes

X-ray ptychography provides exceptional nanoscale resolution and is widely applied in materials science, biology, and nanotechnology. However, its full potential is constrained by the critical challenge of accurately reconstructing images when the illuminating probe is unknown. Conventional iterative methods and deep learning approaches are often suboptimal, particularly under the low-signal conditions inherent to low-dose and high-speed experiments. These limitations compromise reconstruction fidelity and restrict the broader adoption of the technique. In this work, we introduce the Ptychographic Implicit Neural Representation (PtyINR), a self-supervised framework that simultaneously addresses the object and probe recovery problem. By parameterizing both as continuous neural representations, PtyINR performs end-to-end reconstruction directly from raw diffraction patterns without requiring any pre-characterization of the probe. Extensive evaluations demonstrate that PtyINR achieves superior reconstruction quality on both simulated and experimental data, with remarkable robustness under challenging low-signal conditions. Furthermore, PtyINR offers a generalizable, physics-informed framework for addressing probe-dependent inverse problems, making it applicable to a wide range of computational microscopy problems.

Limited-angle x-ray nano-tomography with machine-learning enabled iterative reconstruction engine

A long-standing challenge in tomography is the 'missing wedge' problem, which arises when the acquisition of projection images within a certain angular range is restricted due to geometrical constraints. This incomplete dataset results in significant artifacts and poor resolution in the reconstructed image. To tackle this challenge, we propose an approach dubbed Perception Fused Iterative Tomography Reconstruction Engine, which integrates a convolutional neural network (CNN) with perceptional knowledge as a smart regularizer into an iterative solving engine. We employ the Alternating Direction Method of Multipliers to optimize the solution in both physics and image domains, thereby achieving a physically coherent and visually enhanced result. We demonstrate the effectiveness of the proposed approach using various experimental datasets obtained with different x-ray microscopy techniques. All show significantly improved reconstruction even with a missing wedge of over 100 degrees - a scenario where conventional methods fail. Notably, it also improves the reconstruction in case of sparse projections, despite the network not being specifically trained for that. This demonstrates the robustness and generality of our method of addressing commonly occurring challenges in 3D x-ray imaging applications for real-world problems.