# Attentional Ptycho-Tomography (APT) for three-dimensional nanoscale X-ray imaging with minimal data acquisition and computation time

arXiv: https://arxiv.org/abs/2212.00014 · HTML: https://mlsanity.com/paper/2212.00014/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 66 references that are in the map.
- First posted on arXiv 29 Nov 2022.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [Rethinking Atrous Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1706.05587/) (2017)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Panoptic-DeepLab](https://mlsanity.com/paper/1910.04751/) (2019)
- [Axial-DeepLab: Stand-Alone Axial-Attention for Panoptic Segmentation](https://mlsanity.com/paper/2003.07853/) (2020)
- [ParseNet: Looking Wider to See Better](https://mlsanity.com/paper/1506.04579/) (2015)
- [DeepRED: Deep Image Prior Powered by RED](https://mlsanity.com/paper/1903.10176/) (2019)
- [Computed Tomography Reconstruction Using Deep Image Prior and Learned Reconstruction Methods](https://mlsanity.com/paper/2003.04989/) (2020)
- [Low Photon Count Phase Retrieval Using Deep Learning](https://mlsanity.com/paper/1806.10029/) (2018)
- [High-Resolution Limited-Angle Phase Tomography of Dense Layered Objects Using Deep Neural Networks](https://mlsanity.com/paper/1812.07380/) (2018)
- [Limited-angle tomographic reconstruction of dense layered objects by dynamical machine learning](https://mlsanity.com/paper/2007.10734/) (2020)

## Built on by (most cited first, 2 of 2)

- [Accelerated deep self-supervised ptycho-laminography for three-dimensional nanoscale imaging of integrated circuits](https://mlsanity.com/paper/2304.04597/) (2023)
- [Limited-angle x-ray nano-tomography with machine-learning enabled iterative reconstruction engine](https://mlsanity.com/paper/2503.19248/) (2025)

## Abstract (arXiv)

Noninvasive X-ray imaging of nanoscale three-dimensional objects, e.g. integrated circuits (ICs), generally requires two types of scanning: ptychographic, which is translational and returns estimates of complex electromagnetic field through ICs; and tomographic scanning, which collects complex field projections from multiple angles. Here, we present Attentional Ptycho-Tomography (APT), an approach trained to provide accurate reconstructions of ICs despite incomplete measurements, using a dramatically reduced amount of angular scanning. Training process includes regularizing priors based on typical IC patterns and the physics of X-ray propagation. We demonstrate that APT with 12-time reduced angles achieves fidelity comparable to the gold standard with the original set of angles. With the same set of reduced angles, APT also outperforms baseline reconstruction methods. In our experiments, APT achieves 108-time aggregate reduction in data acquisition and computation without compromising quality. We expect our physics-assisted machine learning framework could also be applied to other branches of nanoscale imaging.