# Accelerated parallel MRI using memory efficient and robust monotone operator learning (MOL)

arXiv: https://arxiv.org/abs/2304.01351 · HTML: https://mlsanity.com/paper/2304.01351/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 13 references that are in the map.
- First posted on arXiv 3 Apr 2023.

## Builds on (most cited first, 10 of 10)

- [Training Deep Nets with Sublinear Memory Cost](https://mlsanity.com/paper/1604.06174/) (2016)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [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)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [CLIP: Cheap Lipschitz Training of Neural Networks](https://mlsanity.com/paper/2103.12531/) (2021)
- [Memory-efficient Learning for Large-scale Computational Imaging -- NeurIPS deep inverse workshop](https://mlsanity.com/paper/1912.05098/) (2019)
- [Improved Model based Deep Learning using Monotone Operator Learning (MOL)](https://mlsanity.com/paper/2111.11380/) (2021)

## Abstract (arXiv)

Model-based deep learning methods that combine imaging physics with learned regularization priors have been emerging as powerful tools for parallel MRI acceleration. The main focus of this paper is to determine the utility of the monotone operator learning (MOL) framework in the parallel MRI setting. The MOL algorithm alternates between a gradient descent step using a monotone convolutional neural network (CNN) and a conjugate gradient algorithm to encourage data consistency. The benefits of this approach include similar guarantees as compressive sensing algorithms including uniqueness, convergence, and stability, while being significantly more memory efficient than unrolled methods. We validate the proposed scheme by comparing it with different unrolled algorithms in the context of accelerated parallel MRI for static and dynamic settings.