# Image Reconstruction for Accelerated MR Scan with Faster Fourier Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2306.02886 · HTML: https://mlsanity.com/paper/2306.02886/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 46 references that are in the map.
- First posted on arXiv 5 Jun 2023.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [Resolution-robust Large Mask Inpainting with Fourier Convolutions](https://mlsanity.com/paper/2109.07161/) (2021)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020)
- [DuDoRNet: Learning a Dual-Domain Recurrent Network for Fast MRI Reconstruction with Deep T1 Prior](https://mlsanity.com/paper/2001.03799/) (2020)
- [Deep Residual Learning for Accelerated MRI using Magnitude and Phase Networks](https://mlsanity.com/paper/1804.00432/) (2018)
- [GrappaNet: Combining Parallel Imaging with Deep Learning for Multi-Coil MRI Reconstruction](https://mlsanity.com/paper/1910.12325/) (2019)
- [Deep Learning with Domain Adaptation for Accelerated Projection-Reconstruction MR](https://mlsanity.com/paper/1703.01135/) (2017)
- [Deep Generalization of Structured Low-Rank Algorithms (Deep-SLR)](https://mlsanity.com/paper/1912.03433/) (2019)
- [Model Learning: Primal Dual Networks for Fast MR imaging](https://mlsanity.com/paper/1908.02426/) (2019)
- [Memory-efficient Learning for Large-scale Computational Imaging -- NeurIPS deep inverse workshop](https://mlsanity.com/paper/1912.05098/) (2019)
- [VolumeNet: A Lightweight Parallel Network for Super-Resolution of Medical Volumetric Data](https://mlsanity.com/paper/2010.08357/) (2020)
- [Dual-Domain Reconstruction Networks with V-Net and K-Net for fast MRI](https://mlsanity.com/paper/2203.05725/) (2022)
- [Physics-informed compressed sensing for PC-MRI: an inverse Navier-Stokes problem](https://mlsanity.com/paper/2207.01466/) (2022)

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

- [MMR-Mamba: Multi-Modal MRI Reconstruction with Mamba and Spatial-Frequency Information Fusion](https://mlsanity.com/paper/2406.18950/) (2024)
- [DuFal: Dual-Frequency-Aware Learning for High-Fidelity Extremely Sparse-view CBCT Reconstruction](https://mlsanity.com/paper/2601.15416/) (2026)

## Abstract (arXiv)

Partial scan is a common approach to accelerate Magnetic Resonance Imaging (MRI) data acquisition in both 2D and 3D settings. However, accurately reconstructing images from partial scan data (i.e., incomplete k-space matrices) remains challenging due to lack of an effectively global receptive field in both spatial and k-space domains. To address this problem, we propose the following: (1) a novel convolutional operator called Faster Fourier Convolution (FasterFC) to replace the two consecutive convolution operations typically used in convolutional neural networks (e.g., U-Net, ResNet). Based on the spectral convolution theorem in Fourier theory, FasterFC employs alternating kernels of size 1 in 3D case) in different domains to extend the dual-domain receptive field to the global and achieves faster calculation speed than traditional Fast Fourier Convolution (FFC). (2) A 2D accelerated MRI method, FasterFC-End-to-End-VarNet, which uses FasterFC to improve the sensitivity maps and reconstruction quality. (3) A multi-stage 3D accelerated MRI method called FasterFC-based Single-to-group Network (FAS-Net) that utilizes a single-to-group algorithm to guide k-space domain reconstruction, followed by FasterFC-based cascaded convolutional neural networks to expand the effective receptive field in the dual-domain. Experimental results on the fastMRI and Stanford MRI Data datasets demonstrate that FasterFC improves the quality of both 2D and 3D reconstruction. Moreover, FAS-Net, as a 3D high-resolution multi-coil (eight) accelerated MRI method, achieves superior reconstruction performance in both qualitative and quantitative results compared with state-of-the-art 2D and 3D methods.