# K-Space Transformer for Undersampled MRI Reconstruction

arXiv: https://arxiv.org/abs/2206.06947 · HTML: https://mlsanity.com/paper/2206.06947/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 36 references that are in the map.
- First posted on arXiv 14 Jun 2022.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Deeply-Supervised Nets](https://mlsanity.com/paper/1409.5185/) (2014)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [DuDoRNet: Learning a Dual-Domain Recurrent Network for Fast MRI Reconstruction with Deep T1 Prior](https://mlsanity.com/paper/2001.03799/) (2020)
- [Swin Transformer for Fast MRI](https://mlsanity.com/paper/2201.03230/) (2022)
- [Spatially-Adaptive Pixelwise Networks for Fast Image Translation](https://mlsanity.com/paper/2012.02992/) (2020)
- [IREM: High-Resolution Magnetic Resonance (MR) Image Reconstruction via Implicit Neural Representation](https://mlsanity.com/paper/2106.15097/) (2021)
- [CoIL: Coordinate-based Internal Learning for Imaging Inverse Problems](https://mlsanity.com/paper/2102.05181/) (2021)
- [Deep De-Aliasing for Fast Compressive Sensing MRI](https://mlsanity.com/paper/1705.07137/) (2017)

## Built on by (most cited first, 3 of 3)

- [Global k-Space Interpolation for Dynamic MRI Reconstruction using Masked Image Modeling](https://mlsanity.com/paper/2307.12672/) (2023)
- [A Comprehensive Survey on Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/2503.07097/) (2025)
- [Towards Globally Predictable k-Space Interpolation: A White-box Transformer Approach](https://mlsanity.com/paper/2508.04051/) (2025)

## Abstract (arXiv)

This paper considers the problem of undersampled MRI reconstruction. We propose a novel Transformer-based framework for directly processing signal in k-space, going beyond the limitation of regular grids as ConvNets do. We adopt an implicit representation of k-space spectrogram, treating spatial coordinates as inputs, and dynamically query the sparsely sampled points to reconstruct the spectrogram, i.e. learning the inductive bias in k-space. To strike a balance between computational cost and reconstruction quality, we build the decoder with hierarchical structure to generate low-resolution and high-resolution outputs respectively. To validate the effectiveness of our proposed method, we have conducted extensive experiments on two public datasets, and demonstrate superior or comparable performance to state-of-the-art approaches.