# Robust partial Fourier reconstruction for diffusion-weighted imaging using a recurrent convolutional neural network

arXiv: https://arxiv.org/abs/2105.09378 · HTML: https://mlsanity.com/paper/2105.09378/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 37 references that are in the map.
- First posted on arXiv 19 May 2021.

## Builds on (most cited first, 18 of 18)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Attention-based Deep Multiple Instance Learning](https://mlsanity.com/paper/1802.04712/) (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)
- [Delving Deeper into Convolutional Networks for Learning Video Representations](https://mlsanity.com/paper/1511.06432/) (2015)
- [Set Transformer: A Framework for Attention-based Permutation-Invariant Neural Networks](https://mlsanity.com/paper/1810.00825/) (2018)
- [Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems](https://mlsanity.com/paper/1704.03488/) (2017)
- [Convolutional Recurrent Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1712.01751/) (2017)
- [A Deep Cascade of Convolutional Neural Networks for MR Image Reconstruction](https://mlsanity.com/paper/1703.00555/) (2017)
- [Recurrent Inference Machines for Solving Inverse Problems](https://mlsanity.com/paper/1706.04008/) (2017)
- [Learning with Known Operators reduces Maximum Training Error Bounds](https://mlsanity.com/paper/1907.01992/) (2019)
- [Precision Learning: Towards Use of Known Operators in Neural Networks](https://mlsanity.com/paper/1712.00374/) (2017)
- [Training a Neural Network for Gibbs and Noise Removal in Diffusion MRI](https://mlsanity.com/paper/1905.04176/) (2019)

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

- [Learned Cone-Beam CT Reconstruction Using Neural Ordinary Differential Equations](https://mlsanity.com/paper/2201.07562/) (2022)
- [Zero-shot self-supervised learning of single breath-hold magnetic resonance cholangiopancreatography (MRCP) reconstruction](https://mlsanity.com/paper/2508.09200/) (2025)

## Abstract (arXiv)

Purpose: To develop an algorithm for robust partial Fourier (PF) reconstruction applicable to diffusion-weighted (DW) images with non-smooth phase variations. Methods: Based on an unrolled proximal splitting algorithm, a neural network architecture is derived which alternates between data consistency operations and regularization implemented by recurrent convolutions. In order to exploit correlations, multiple repetitions of the same slice are jointly reconstructed under consideration of permutation-equivariance. The algorithm is trained on DW liver data of 60 volunteers and evaluated on retrospectively and prospectively sub-sampled data of different anatomies and resolutions. Results: The proposed method is able to significantly outperform conventional PF techniques on retrospectively sub-sampled data in terms of quantitative measures as well as perceptual image quality. In this context, joint reconstruction of repetitions as well as the particular type of recurrent network unrolling are found to be beneficial with respect to reconstruction quality. On prospectively PF-sampled data, the proposed method enables DW imaging with higher signal without sacrificing image resolution or introducing additional artifacts. Alternatively, it can be used to counter the TE increase in acquisitions with higher resolution. Further, generalizability can be shown to prospective brain data exhibiting anatomies and contrasts not present in the training set. Conclusion: This work demonstrates that robust PF reconstruction of DW data is feasible even at strong PF factors in anatomies prone to phase variations. Since the proposed method does not rely on smoothness priors of the phase but uses learned recurrent convolutions instead, artifacts of conventional PF methods can be avoided.