# Deep Learning-based MRI Reconstruction with Artificial Fourier Transform Network (AFTNet)

arXiv: https://arxiv.org/abs/2312.10892 · HTML: https://mlsanity.com/paper/2312.10892/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 38 references that are in the map.
- First posted on arXiv 18 Dec 2023.

## Builds on (most cited first, 12 of 12)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Learning in the Frequency Domain](https://mlsanity.com/paper/2002.12416/) (2020)
- [On Complex Valued Convolutional Neural Networks](https://mlsanity.com/paper/1602.09046/) (2016)
- [A mathematical motivation for complex-valued convolutional networks](https://mlsanity.com/paper/1503.03438/) (2015)

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

- [A Comprehensive Survey on Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/2503.07097/) (2025)
- [PAS-Mamba: Phase-Amplitude-Spatial State Space Model for MRI Reconstruction](https://mlsanity.com/paper/2601.14530/) (2026)

## Abstract (arXiv)

Deep complex-valued neural networks (CVNNs) provide a powerful way to leverage complex number operations and representations and have succeeded in several phase-based applications. However, previous networks have not fully explored the impact of complex-valued networks in the frequency domain. Here, we introduce a unified complex-valued deep learning framework-Artificial Fourier Transform Network (AFTNet)-which combines domain-manifold learning and CVNNs. AFTNet can be readily used to solve image inverse problems in domain transformation, especially for accelerated magnetic resonance imaging (MRI) reconstruction and other applications. While conventional methods typically utilize magnitude images or treat the real and imaginary components of k-space data as separate channels, our approach directly processes raw k-space data in the frequency domain, utilizing complex-valued operations. This allows for a mapping between the frequency (k-space) and image domain to be determined through cross-domain learning. We show that AFTNet achieves superior accelerated MRI reconstruction compared to existing approaches. Furthermore, our approach can be applied to various tasks, such as denoised magnetic resonance spectroscopy (MRS) reconstruction and datasets with various contrasts. The AFTNet presented here is a valuable preprocessing component for different preclinical studies and provides an innovative alternative for solving inverse problems in imaging and spectroscopy. The code is available at: https://github.com/yanting-yang/AFT-Net.