# Variable Augmented Network for Invertible MR Coil Compression

arXiv: https://arxiv.org/abs/2201.07428 · HTML: https://mlsanity.com/paper/2201.07428/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 47 references that are in the map.
- First posted on arXiv 19 Jan 2022.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [Learning to See in the Dark](https://mlsanity.com/paper/1805.01934/) (2018)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [Towards Fast Computation of Certified Robustness for ReLU Networks](https://mlsanity.com/paper/1804.09699/) (2018)
- [Stochastic Gradient Descent Optimizes Over-parameterized Deep ReLU Networks](https://mlsanity.com/paper/1811.08888/) (2018)
- [Sum-of-Squares Polynomial Flow](https://mlsanity.com/paper/1905.02325/) (2019)

## Abstract (arXiv)

A large number of coils are able to provide enhanced signal-to-noise ratio and improve imaging performance in parallel imaging. Nevertheless, the increasing growth of coil number simultaneously aggravates the drawbacks of data storage and reconstruction speed, especially in some iterative reconstructions. Coil compression addresses these issues by generating fewer virtual coils. In this work, a novel variable augmentation network for invertible coil compression termed VAN-ICC is presented. It utilizes inherent reversibility of normalizing flow-based models for high-precision compression and invertible recovery. By employing the variable augmentation technology to image/k-space variables from multi-coils, VAN-ICC trains invertible networks by finding an invertible and bijective function, which can map the original data to the compressed counterpart and vice versa. Experiments conducted on both fully-sampled and under-sampled data verified the effectiveness and flexibility of VAN-ICC. Quantitative and qualitative comparisons with traditional non-deep learning-based approaches demonstrated that VAN-ICC can carry much higher compression effects. Additionally, its performance is not susceptible to different number of virtual coils.