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

arXiv: https://arxiv.org/abs/2509.04402 · HTML: https://mlsanity.com/paper/2509.04402/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 62 references that are in the map.
- First posted on arXiv 4 Sep 2025.

## Builds on (most cited first, 19 of 19)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Recovery of Continuous 3D Refractive Index Maps from Discrete Intensity-Only Measurements using Neural Fields](https://mlsanity.com/paper/2112.00002/) (2021)
- [Deep learning at the edge enables real-time streaming ptychographic imaging](https://mlsanity.com/paper/2209.09408/) (2022)
- [Physics Constrained Unsupervised Deep Learning for Rapid, High Resolution Scanning Coherent Diffraction Reconstruction](https://mlsanity.com/paper/2306.11014/) (2023)
- [Coordinate-based neural representations for computational adaptive optics in widefield microscopy](https://mlsanity.com/paper/2307.03812/) (2023)
- [PtychoDV: Vision Transformer-Based Deep Unrolling Network for Ptychographic Image Reconstruction](https://mlsanity.com/paper/2310.07504/) (2023)
- [Adorym: A multi-platform generic x-ray image reconstruction framework based on automatic differentiation](https://mlsanity.com/paper/2012.12686/) (2020)
- [SHARP: a distributed, GPU-based ptychographic solver](https://mlsanity.com/paper/1602.01448/) (2016)
- [Using Automatic Differentiation as a General Framework for Ptychographic Reconstruction](https://mlsanity.com/paper/1902.03920/) (2019)
- [Three dimensions, two microscopes, one code: automatic differentiation for x-ray nanotomography beyond the depth of focus limit](https://mlsanity.com/paper/1905.10433/) (2019)
- [Projected Multi-Agent Consensus Equilibrium (PMACE) with Application to Ptychography](https://mlsanity.com/paper/2303.15679/) (2023)
- [Predicting ptychography probe positions using single-shot phase retrieval neural network](https://mlsanity.com/paper/2405.20910/) (2024)
- [Low-dose cryo electron ptychography via non-convex Bayesian optimization](https://mlsanity.com/paper/1702.05732/) (2017)
- [A semi-implicit relaxed Douglas-Rachford algorithm (sir-DR) for Ptychograhpy](https://mlsanity.com/paper/1906.01875/) (2019)
- [Ptychographic phase-retrieval by proximal algorithms](https://mlsanity.com/paper/1909.06482/) (2019)
- [Fidelity-preserving enhancement of ptychography with foundational text-to-image models](https://mlsanity.com/paper/2509.04513/) (2025)

## Built on by (most cited first, 1 of 1)

- [Towards generalizable deep ptychography neural networks](https://mlsanity.com/paper/2509.25104/) (2025)

## Abstract (arXiv)

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.