# Three-dimensional Coherent X-ray Diffraction Imaging via Deep Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2103.00001 · HTML: https://mlsanity.com/paper/2103.00001/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2021.

## Built on by (most cited first, 10 of 10)

- [Deep learning at the edge enables real-time streaming ptychographic imaging](https://mlsanity.com/paper/2209.09408/) (2022)
- [Practical Phase Retrieval Using Double Deep Image Priors](https://mlsanity.com/paper/2211.00799/) (2022)
- [SiSPRNet: End-to-End Learning for Single-Shot Phase Retrieval](https://mlsanity.com/paper/2205.11434/) (2022)
- [Deep-learning real-time phase retrieval of imperfect diffraction patterns from X-ray free-electron lasers](https://mlsanity.com/paper/2409.15784/) (2024)
- [Towards Practical Single-shot Phase Retrieval with Physics-Driven Deep Neural Network](https://mlsanity.com/paper/2208.08604/) (2022)
- [Machine learning for classifying and interpreting coherent X-ray speckle patterns](https://mlsanity.com/paper/2211.08194/) (2022)
- [Coordinate-based Neural Network for Fourier Phase Retrieval](https://mlsanity.com/paper/2311.14925/) (2023)
- [Augmenting x-ray single particle imaging reconstruction with self-supervised machine learning](https://mlsanity.com/paper/2311.16652/) (2023)
- [Res-U2Net: Untrained Deep Learning for Phase Retrieval and Image Reconstruction](https://mlsanity.com/paper/2404.06657/) (2024)
- [OPENXRD: A Comprehensive Benchmark Framework for LLM/MLLM XRD Question Answering](https://mlsanity.com/paper/2507.09155/) (2025)

## Abstract (arXiv)

As a critical component of coherent X-ray diffraction imaging (CDI), phase retrieval has been extensively applied in X-ray structural science to recover the 3D morphological information inside measured particles. Despite meeting all the oversampling requirements of Sayre and Shannon, current phase retrieval approaches still have trouble achieving a unique inversion of experimental data in the presence of noise. Here, we propose to overcome this limitation by incorporating a 3D Machine Learning (ML) model combining (optional) supervised learning with transfer learning. The trained ML model can rapidly provide an immediate result with high accuracy which could benefit real-time experiments, and the predicted result can be further refined with transfer learning. More significantly, the proposed ML model can be used without any prior training to learn the missing phases of an image based on minimization of an appropriate 'loss function' alone. We demonstrate significantly improved performance with experimental Bragg CDI data over traditional iterative phase retrieval algorithms.