# Deep variational network for rapid 4D flow MRI reconstruction

arXiv: https://arxiv.org/abs/2004.09610 · HTML: https://mlsanity.com/paper/2004.09610/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2020.

## Built on by (most cited first, 11 of 11)

- [AI-based Reconstruction for Fast MRI -- A Systematic Review and Meta-analysis](https://mlsanity.com/paper/2112.12744/) (2021)
- [Stable Deep MRI Reconstruction using Generative Priors](https://mlsanity.com/paper/2210.13834/) (2022)
- [One for Multiple: Physics-informed Synthetic Data Boosts Generalizable Deep Learning for Fast MRI Reconstruction](https://mlsanity.com/paper/2307.13220/) (2023)
- [Implicit neural representations for unsupervised super-resolution and denoising of 4D flow MRI](https://mlsanity.com/paper/2302.12835/) (2023)
- [Deep-ER: Deep Learning ECCENTRIC Reconstruction for fast high-resolution neurometabolic imaging](https://mlsanity.com/paper/2409.18303/) (2024)
- [Variational volume reconstruction with the Deep Ritz Method](https://mlsanity.com/paper/2508.08309/) (2025)
- [Simultaneous boundary shape estimation and velocity field de-noising in Magnetic Resonance Velocimetry using Physics-informed Neural Networks](https://mlsanity.com/paper/2107.07863/) (2021)
- [Physics-informed Deep Diffusion MRI Reconstruction with Synthetic Data: Break Training Data Bottleneck in Artificial Intelligence](https://mlsanity.com/paper/2210.11388/) (2022)
- [FlowMoDL: Model-Based Deep Learning with Conjugate-Gradient Data Consistency for Highly Accelerated 4D Flow MRI Reconstruction](https://mlsanity.com/paper/2608.25828/) (2026)
- [CLEAR: Complex Learned Explicit Analytical Regularization for Ultra-Accelerated 4D Flow CMR Reconstruction](https://mlsanity.com/paper/2609.22950/) (2026)
- [Joint Supervised and Self-Supervised Training with Acquisition-Robust Techniques for Accelerated 4D Flow MRI Reconstruction](https://mlsanity.com/paper/2609.38644/) (2026)

## Abstract (arXiv)

Phase-contrast magnetic resonance imaging (MRI) provides time-resolved quantification of blood flow dynamics that can aid clinical diagnosis. Long in vivo scan times due to repeated three-dimensional (3D) volume sampling over cardiac phases and breathing cycles necessitate accelerated imaging techniques that leverage data correlations. Standard compressed sensing reconstruction methods require tuning of hyperparameters and are computationally expensive, which diminishes the potential reduction of examination times. We propose an efficient model-based deep neural reconstruction network and evaluate its performance on clinical aortic flow data. The network is shown to reconstruct undersampled 4D flow MRI data in under a minute on standard consumer hardware. Remarkably, the relatively low amounts of tunable parameters allowed the network to be trained on images from 11 reference scans while generalizing well to retrospective and prospective undersampled data for various acceleration factors and anatomies.