# A Projection-Based K-space Transformer Network for Undersampled Radial MRI Reconstruction with Limited Training Subjects

arXiv: https://arxiv.org/abs/2206.07219 · HTML: https://mlsanity.com/paper/2206.07219/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 31 references that are in the map.
- First posted on arXiv 15 Jun 2022.

## Builds on (most cited first, 13 of 13)

- [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)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Image Transformer](https://mlsanity.com/paper/1802.05751/) (2018)
- [Compressed Sensing MRI Reconstruction using a Generative Adversarial Network with a Cyclic Loss](https://mlsanity.com/paper/1709.00753/) (2017)
- [Real-time Cardiovascular MR with Spatio-temporal Artifact Suppression using Deep Learning - Proof of Concept in Congenital Heart Disease](https://mlsanity.com/paper/1803.05192/) (2018)
- [Spatio-Temporal Deep Learning-Based Undersampling Artefact Reduction for 2D Radial Cine MRI with Limited Data](https://mlsanity.com/paper/1904.01574/) (2019)
- [Deep De-Aliasing for Fast Compressive Sensing MRI](https://mlsanity.com/paper/1705.07137/) (2017)
- [An End-To-End-Trainable Iterative Network Architecture for Accelerated Radial Multi-Coil 2D Cine MR Image Reconstruction](https://mlsanity.com/paper/2102.00783/) (2021)
- [Reconstruction of Undersampled 3D Non-Cartesian Image-Based Navigators for Coronary MRA Using an Unrolled Deep Learning Model](https://mlsanity.com/paper/1910.11414/) (2019)

## Built on by (most cited first, 4 of 4)

- [Transformers in Healthcare: A Survey](https://mlsanity.com/paper/2307.00067/) (2023)
- [Global k-Space Interpolation for Dynamic MRI Reconstruction using Masked Image Modeling](https://mlsanity.com/paper/2307.12672/) (2023)
- [Constrained Probabilistic Mask Learning for Task-specific Undersampled MRI Reconstruction](https://mlsanity.com/paper/2305.16376/) (2023)
- [A Comprehensive Survey on Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/2503.07097/) (2025)

## Abstract (arXiv)

The recent development of deep learning combined with compressed sensing enables fast reconstruction of undersampled MR images and has achieved state-of-the-art performance for Cartesian k-space trajectories. However, non-Cartesian trajectories such as the radial trajectory need to be transformed onto a Cartesian grid in each iteration of the network training, slowing down the training process and posing inconvenience and delay during training. Multiple iterations of nonuniform Fourier transform in the networks offset the deep learning advantage of fast inference. Current approaches typically either work on image-to-image networks or grid the non-Cartesian trajectories before the network training to avoid the repeated gridding process. However, the image-to-image networks cannot ensure the k-space data consistency in the reconstructed images and the pre-processing of non-Cartesian k-space leads to gridding errors which cannot be compensated by the network training. Inspired by the Transformer network to handle long-range dependencies in sequence transduction tasks, we propose to rearrange the radial spokes to sequential data based on the chronological order of acquisition and use the Transformer to predict unacquired radial spokes from acquired ones. We propose novel data augmentation methods to generate a large amount of training data from a limited number of subjects. The network can be generated to different anatomical structures. Experimental results show superior performance of the proposed framework compared to state-of-the-art deep neural networks.