# Recurrent Variational Network: A Deep Learning Inverse Problem Solver applied to the task of Accelerated MRI Reconstruction arXiv: https://arxiv.org/abs/2111.09639 ยท HTML: https://mlsanity.com/paper/2111.09639/ ## Key facts - Cited by 34 papers in the map (data through 14 Oct 2026). - Builds on 14 of its 46 references that are in the map. - First posted on arXiv 18 Nov 2021. ## Builds on (most cited first, 14 of 14) - [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019) - [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017) - [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015) - [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018) - [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017) - [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017) - [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020) - [Convolutional Recurrent Neural Networks for Polyphonic Sound Event Detection](https://mlsanity.com/paper/1702.06286/) (2017) - [Recurrent Inference Machines for Solving Inverse Problems](https://mlsanity.com/paper/1706.04008/) (2017) - [Partial Convolution based Padding](https://mlsanity.com/paper/1811.11718/) (2018) - [LORAKI: Autocalibrated Recurrent Neural Networks for Autoregressive MRI Reconstruction in k-Space](https://mlsanity.com/paper/1904.09390/) (2019) - [Multi-Coil MRI Reconstruction Challenge -- Assessing Brain MRI Reconstruction Models and their Generalizability to Varying Coil Configurations](https://mlsanity.com/paper/2011.07952/) (2020) - [XPDNet for MRI Reconstruction: an application to the 2020 fastMRI challenge](https://mlsanity.com/paper/2010.07290/) (2020) - [Dual-domain Cascade of U-nets for Multi-channel Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/1911.01458/) (2019) ## Built on by (most cited first, 30 of 34) - [MedShapeNet -- A Large-Scale Dataset of 3D Medical Shapes for Computer Vision](https://mlsanity.com/paper/2308.16139/) (2023) - [Progressive Divide-and-Conquer via Subsampling Decomposition for Accelerated MRI](https://mlsanity.com/paper/2403.10064/) (2024) - [On Retrospective k-space Subsampling schemes For Deep MRI Reconstruction](https://mlsanity.com/paper/2301.08365/) (2023) - [vSHARP: variable Splitting Half-quadratic Admm algorithm for Reconstruction of inverse-Problems](https://mlsanity.com/paper/2309.09954/) (2023) - [MambaRecon: MRI Reconstruction with Structured State Space Models](https://mlsanity.com/paper/2409.12401/) (2024) - [Deep Cardiac MRI Reconstruction with ADMM](https://mlsanity.com/paper/2310.06628/) (2023) - [Noise Level Adaptive Diffusion Model for Robust Reconstruction of Accelerated MRI](https://mlsanity.com/paper/2403.05245/) (2024) - [Spatial and Modal Optimal Transport for Fast Cross-Modal MRI Reconstruction](https://mlsanity.com/paper/2305.02774/) (2023) - [Robust Physics-based Deep MRI Reconstruction Via Diffusion Purification](https://mlsanity.com/paper/2309.05794/) (2023) - [Joint Supervised and Self-supervised Learning for MRI Reconstruction](https://mlsanity.com/paper/2311.15856/) (2023) - [Fast MRI Reconstruction via Edge Attention](https://mlsanity.com/paper/2304.11400/) (2023) - [CAMP-Net: Consistency-Aware Multi-Prior Network for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2306.11238/) (2023) - [Score-based Generative Priors Guided Model-driven Network for MRI Reconstruction](https://mlsanity.com/paper/2405.02958/) (2024) - [UGoDIT: Unsupervised Group Deep Image Prior Via Transferable Weights](https://mlsanity.com/paper/2505.11720/) (2025) - [HyperCoil-Recon: A Hypernetwork-based Adaptive Coil Configuration Task Switching Network for MRI Reconstruction](https://mlsanity.com/paper/2308.04821/) (2023) - [End-to-end Adaptive Dynamic Subsampling and Reconstruction for Cardiac MRI](https://mlsanity.com/paper/2403.10346/) (2024) - [Joint Edge Optimization Deep Unfolding Network for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2405.05564/) (2024) - [Reconstruction of Cardiac Cine MRI Using Motion-Guided Deformable Alignment and Multi-Resolution Fusion](https://mlsanity.com/paper/2303.04968/) (2023) - [Uncertainty-Aware Null Space Networks for Data-Consistent Image Reconstruction](https://mlsanity.com/paper/2304.06955/) (2023) - [SDLFormer: A Sparse and Dense Locality-enhanced Transformer for Accelerated MR Image Reconstruction](https://mlsanity.com/paper/2308.04262/) (2023) - [NoSENSE: Learned unrolled cardiac MRI reconstruction without explicit sensitivity maps](https://mlsanity.com/paper/2309.15608/) (2023) - [Relaxometry Guided Quantitative Cardiac Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/2403.00549/) (2024) - [ATOMMIC: An Advanced Toolbox for Multitask Medical Imaging Consistency to facilitate Artificial Intelligence applications from acquisition to analysis in Magnetic Resonance Imaging](https://mlsanity.com/paper/2404.19665/) (2024) - [A Comprehensive Survey on Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/2503.07097/) (2025) - [Equivariant Multiscale Learned Invertible Reconstruction for Cone Beam CT](https://mlsanity.com/paper/2401.11256/) (2024) - [Real-time cardiac cine MRI -- A comparison of a diffusion probabilistic model with alternative state-of-the-art image reconstruction techniques for undersampled spiral acquisitions](https://mlsanity.com/paper/2410.04843/) (2024) - [Deep End-to-end Adaptive k-Space Sampling, Reconstruction, and Registration for Dynamic MRI](https://mlsanity.com/paper/2411.18249/) (2024) - [Training-Free Adversarial Robustness in Computational MRI](https://mlsanity.com/paper/2501.01908/) (2025) - [UEPS: Robust and Efficient MRI Reconstruction](https://mlsanity.com/paper/2603.18572/) (2026) - [Are Natural-Domain Foundation Models Effective for Accelerated Cardiac MRI Reconstruction?](https://mlsanity.com/paper/2604.22557/) (2026) ## Abstract (arXiv) Magnetic Resonance Imaging can produce detailed images of the anatomy and physiology of the human body that can assist doctors in diagnosing and treating pathologies such as tumours. However, MRI suffers from very long acquisition times that make it susceptible to patient motion artifacts and limit its potential to deliver dynamic treatments. Conventional approaches such as Parallel Imaging and Compressed Sensing allow for an increase in MRI acquisition speed by reconstructing MR images from sub-sampled MRI data acquired using multiple receiver coils. Recent advancements in Deep Learning combined with Parallel Imaging and Compressed Sensing techniques have the potential to produce high-fidelity reconstructions from highly accelerated MRI data. In this work we present a novel Deep Learning-based Inverse Problem solver applied to the task of Accelerated MRI Reconstruction, called the Recurrent Variational Network (RecurrentVarNet), by exploiting the properties of Convolutional Recurrent Neural Networks and unrolled algorithms for solving Inverse Problems. The RecurrentVarNet consists of multiple recurrent blocks, each responsible for one iteration of the unrolled variational optimization scheme for solving the inverse problem of multi-coil Accelerated MRI Reconstruction. Contrary to traditional approaches, the optimization steps are performed in the observation domain (k-space) instead of the image domain. Each block of the RecurrentVarNet refines the observed k-space and comprises a data consistency term and a recurrent unit which takes as input a learned hidden state and the prediction of the previous block. Our proposed method achieves new state of the art qualitative and quantitative reconstruction results on 5-fold and 10-fold accelerated data from a public multi-coil brain dataset, outperforming previous conventional and deep learning-based approaches.