# Q-RBSA: High-Resolution 3D EBSD Map Generation Using An Efficient Quaternion Transformer Network

arXiv: https://arxiv.org/abs/2303.10722 · HTML: https://mlsanity.com/paper/2303.10722/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 47 references that are in the map.
- First posted on arXiv 19 Mar 2023.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Deep Learning for Image Super-resolution: A Survey](https://mlsanity.com/paper/1902.06068/) (2019)
- [Deep Quaternion Networks](https://mlsanity.com/paper/1712.04604/) (2017)
- [Quaternion Convolutional Neural Networks](https://mlsanity.com/paper/1903.00658/) (2019)
- [Quaternion Convolutional Neural Networks for End-to-End Automatic Speech Recognition](https://mlsanity.com/paper/1806.07789/) (2018)
- [A Framework for Dynamic Image Sampling Based on Supervised Learning (SLADS)](https://mlsanity.com/paper/1703.04653/) (2017)
- [Reduced Electron Exposure for Energy-Dispersive Spectroscopy using Dynamic Sampling](https://mlsanity.com/paper/1707.03848/) (2017)

## Built on by (most cited first, 6 of 6)

- [Masked LoGoNet: Fast and Accurate 3D Image Analysis for Medical Domain](https://mlsanity.com/paper/2402.06190/) (2024)
- [Learning Metal Microstructural Heterogeneity through Spatial Mapping of Diffraction Latent Space Features](https://mlsanity.com/paper/2501.18064/) (2025)
- [F2IDiff: Real-world Image Super-resolution using Feature to Image Diffusion Foundation Model](https://mlsanity.com/paper/2512.24473/) (2025)
- [PolyMicros: Bootstrapping a Foundation Model for Polycrystalline Material Structure](https://mlsanity.com/paper/2506.11055/) (2025)
- [Towards Space Group Determination from EBSD Patterns: The Role of Deep Learning and High-throughput Dynamical Simulations](https://mlsanity.com/paper/2504.21331/) (2025)
- [Symmetry-aware super-resolution of crystal orientation maps via invariant latent-space learning](https://mlsanity.com/paper/2609.10898/) (2026)

## Abstract (arXiv)

Gathering 3D material microstructural information is time-consuming, expensive, and energy-intensive. Acquisition of 3D data has been accelerated by developments in serial sectioning instrument capabilities; however, for crystallographic information, the electron backscatter diffraction (EBSD) imaging modality remains rate limiting. We propose a physics-based efficient deep learning framework to reduce the time and cost of collecting 3D EBSD maps. Our framework uses a quaternion residual block self-attention network (QRBSA) to generate high-resolution 3D EBSD maps from sparsely sectioned EBSD maps. In QRBSA, quaternion-valued convolution effectively learns local relations in orientation space, while self-attention in the quaternion domain captures long-range correlations. We apply our framework to 3D data collected from commercially relevant titanium alloys, showing both qualitatively and quantitatively that our method can predict missing samples (EBSD information between sparsely sectioned mapping points) as compared to high-resolution ground truth 3D EBSD maps.