# An End-To-End-Trainable Iterative Network Architecture for Accelerated Radial Multi-Coil 2D Cine MR Image Reconstruction

arXiv: https://arxiv.org/abs/2102.00783 · HTML: https://mlsanity.com/paper/2102.00783/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 53 references that are in the map.
- First posted on arXiv 1 Feb 2021.

## Builds on (most cited first, 17 of 17)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [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)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019)
- [Convolutional Recurrent Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1712.01751/) (2017)
- [Deep learning for undersampled MRI reconstruction](https://mlsanity.com/paper/1709.02576/) (2017)
- [Deep Learning Methods for Parallel Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/1904.01112/) (2019)
- [A Haar Wavelet-Based Perceptual Similarity Index for Image Quality Assessment](https://mlsanity.com/paper/1607.06140/) (2016)
- [VS-Net: Variable splitting network for accelerated parallel MRI reconstruction](https://mlsanity.com/paper/1907.10033/) (2019)
- [Learning with Known Operators reduces Maximum Training Error Bounds](https://mlsanity.com/paper/1907.01992/) (2019)
- [Real-time Cardiovascular MR with Spatio-temporal Artifact Suppression using Deep Learning - Proof of Concept in Congenital Heart Disease](https://mlsanity.com/paper/1803.05192/) (2018)
- [Spatio-Temporal Deep Learning-Based Undersampling Artefact Reduction for 2D Radial Cine MRI with Limited Data](https://mlsanity.com/paper/1904.01574/) (2019)
- [k-t NEXT: Dynamic MR Image Reconstruction Exploiting Spatio-temporal Correlations](https://mlsanity.com/paper/1907.09425/) (2019)
- [Reconstruction of Undersampled 3D Non-Cartesian Image-Based Navigators for Coronary MRA Using an Unrolled Deep Learning Model](https://mlsanity.com/paper/1910.11414/) (2019)

## Built on by (most cited first, 7 of 7)

- [PINQI: An End-to-End Physics-Informed Approach to Learned Quantitative MRI Reconstruction](https://mlsanity.com/paper/2306.11023/) (2023)
- [Deep, Deep Learning with BART](https://mlsanity.com/paper/2202.14005/) (2022)
- [A Projection-Based K-space Transformer Network for Undersampled Radial MRI Reconstruction with Limited Training Subjects](https://mlsanity.com/paper/2206.07219/) (2022)
- [Data-Consistent Non-Cartesian Deep Subspace Learning for Efficient Dynamic MR Image Reconstruction](https://mlsanity.com/paper/2205.01770/) (2022)
- [Convolutional Analysis Operator Learning by End-To-End Training of Iterative Neural Networks](https://mlsanity.com/paper/2203.02166/) (2022)
- [Convolutional Dictionary Learning by End-To-End Training of Iterative Neural Networks](https://mlsanity.com/paper/2206.04447/) (2022)
- [Cine cardiac MRI reconstruction using a convolutional recurrent network with refinement](https://mlsanity.com/paper/2309.13385/) (2023)

## Abstract (arXiv)

Purpose: Iterative Convolutional Neural Networks (CNNs) which resemble unrolled learned iterative schemes have shown to consistently deliver state-of-the-art results for image reconstruction problems across different imaging modalities. However, because these methodes include the forward model in the architecture, their applicability is often restricted to either relatively small reconstruction problems or to problems with operators which are computationally cheap to compute. As a consequence, they have so far not been applied to dynamic non-Cartesian multi-coil reconstruction problems. Methods: In this work, we propose a CNN-architecture for image reconstruction of accelerated 2D radial cine MRI with multiple receiver coils. The network is based on a computationally light CNN-component and a subsequent conjugate gradient (CG) method which can be jointly trained end-to-end using an efficient training strategy. We investigate the proposed training-strategy and compare our method to other well-known reconstruction techniques with learned and non-learned regularization methods. Results: Our proposed method outperforms all other methods based on non-learned regularization. Further, it performs similar or better than a CNN-based method employing a 3D U-Net and a method using adaptive dictionary learning. In addition, we empirically demonstrate that even by training the network with only iteration, it is possible to increase the length of the network at test time and further improve the results. Conclusions: End-to-end training allows to highly reduce the number of trainable parameters of and stabilize the reconstruction network. Further, because it is possible to change the length of the network at test time, the need to find a compromise between the complexity of the CNN-block and the number of iterations in each CG-block becomes irrelevant.