# PARCEL: Physics-based Unsupervised Contrastive Representation Learning for Multi-coil MR Imaging

arXiv: https://arxiv.org/abs/2202.01494 · HTML: https://mlsanity.com/paper/2202.01494/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 49 references that are in the map.
- First posted on arXiv 3 Feb 2022.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (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)
- [Deep Learning Methods for Parallel Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/1904.01112/) (2019)
- [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)
- [Multi-Modal Transformer for Accelerated MR Imaging](https://mlsanity.com/paper/2106.14248/) (2021)
- [Multi-Contrast MRI Super-Resolution via a Multi-Stage Integration Network](https://mlsanity.com/paper/2105.08949/) (2021)
- [Momentum-Net: Fast and convergent iterative neural network for inverse problems](https://mlsanity.com/paper/1907.11818/) (2019)
- [Self-Supervised Learning for MRI Reconstruction with a Parallel Network Training Framework](https://mlsanity.com/paper/2109.12502/) (2021)
- [Deep learning for fast MR imaging: a review for learning reconstruction from incomplete k-space data](https://mlsanity.com/paper/2012.08931/) (2020)
- [Dual-Octave Convolution for Accelerated Parallel MR Image Reconstruction](https://mlsanity.com/paper/2104.05345/) (2021)
- [DONet: Dual-Octave Network for Fast MR Image Reconstruction](https://mlsanity.com/paper/2105.05980/) (2021)

## Built on by (most cited first, 8 of 8)

- [Spatiotemporal implicit neural representation for unsupervised dynamic MRI reconstruction](https://mlsanity.com/paper/2301.00127/) (2022)
- [A theoretical framework for self-supervised MR image reconstruction using sub-sampling via variable density Noisier2Noise](https://mlsanity.com/paper/2205.10278/) (2022)
- [Self-Supervised Scalable Deep Compressed Sensing](https://mlsanity.com/paper/2308.13777/) (2023)
- [SelfCoLearn: Self-supervised collaborative learning for accelerating dynamic MR imaging](https://mlsanity.com/paper/2208.03904/) (2022)
- [Benchmarking Self-Supervised Learning Methods for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2502.14009/) (2025)
- [RobNODDI: Robust NODDI Parameter Estimation with Adaptive Sampling under Continuous Representation](https://mlsanity.com/paper/2408.01944/) (2024)
- [SamRobNODDI: Q-Space Sampling-Augmented Continuous Representation Learning for Robust and Generalized NODDI](https://mlsanity.com/paper/2411.06444/) (2024)
- [Re-Visible Dual-Domain Self-Supervised Deep Unfolding Network for MRI Reconstruction](https://mlsanity.com/paper/2501.03737/) (2025)

## Abstract (arXiv)

With the successful application of deep learning to magnetic resonance (MR) imaging, parallel imaging techniques based on neural networks have attracted wide attention. However, in the absence of high-quality, fully sampled datasets for training, the performance of these methods is limited. And the interpretability of models is not strong enough. To tackle this issue, this paper proposes a Physics-bAsed unsupeRvised Contrastive rEpresentation Learning (PARCEL) method to speed up parallel MR imaging. Specifically, PARCEL has a parallel framework to contrastively learn two branches of model-based unrolling networks from augmented undersampled multi-coil k-space data. A sophisticated co-training loss with three essential components has been designed to guide the two networks in capturing the inherent features and representations for MR images. And the final MR image is reconstructed with the trained contrastive networks. PARCEL was evaluated on two vivo datasets and compared to five state-of-the-art methods. The results show that PARCEL is able to learn essential representations for accurate MR reconstruction without relying on fully sampled datasets.