# An Optimal Control Framework for Joint-channel Parallel MRI Reconstruction without Coil Sensitivities

arXiv: https://arxiv.org/abs/2109.09738 · HTML: https://mlsanity.com/paper/2109.09738/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 69 references that are in the map.
- First posted on arXiv 20 Sep 2021.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [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)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [Compressed Sensing MRI Reconstruction using a Generative Adversarial Network with a Cyclic Loss](https://mlsanity.com/paper/1709.00753/) (2017)
- [Deep Learning Methods for Parallel Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/1904.01112/) (2019)
- [Maximum Principle Based Algorithms for Deep Learning](https://mlsanity.com/paper/1710.09513/) (2017)
- [Deep Learning via Dynamical Systems: An Approximation Perspective](https://mlsanity.com/paper/1912.10382/) (2019)
- [GrappaNet: Combining Parallel Imaging with Deep Learning for Multi-Coil MRI Reconstruction](https://mlsanity.com/paper/1910.12325/) (2019)
- [An Optimal Control Approach to Deep Learning and Applications to Discrete-Weight Neural Networks](https://mlsanity.com/paper/1803.01299/) (2018)
- [Model Learning: Primal Dual Networks for Fast MR imaging](https://mlsanity.com/paper/1908.02426/) (2019)
- [An Adaptive Intelligence Algorithm for Undersampled Knee MRI Reconstruction](https://mlsanity.com/paper/2004.07339/) (2020)
- [Unified cross-modality feature disentangler for unsupervised multi-domain MRI abdomen organs segmentation](https://mlsanity.com/paper/2007.09669/) (2020)
- [MRI Image Reconstruction via Learning Optimization Using Neural ODEs](https://mlsanity.com/paper/2006.13825/) (2020)
- [Cross-Domain Medical Image Translation by Shared Latent Gaussian Mixture Model](https://mlsanity.com/paper/2007.07230/) (2020)
- [A Hybrid Frequency-domain/Image-domain Deep Network for Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/1810.12473/) (2018)
- [pISTA-SENSE-ResNet for Parallel MRI Reconstruction](https://mlsanity.com/paper/1910.00650/) (2019)
- [Deep Parallel MRI Reconstruction Network Without Coil Sensitivities](https://mlsanity.com/paper/2008.01410/) (2020)
- [Model-based Convolutional De-Aliasing Network Learning for Parallel MR Imaging](https://mlsanity.com/paper/1908.02054/) (2019)
- [GRAPPA-GANs for Parallel MRI Reconstruction](https://mlsanity.com/paper/2101.03135/) (2021)

## Built on by (most cited first, 10 of 10)

- [Harnessing Earnings Reports for Stock Predictions: A QLoRA-Enhanced LLM Approach](https://mlsanity.com/paper/2408.06634/) (2024)
- [Diffusion Modeling with Domain-conditioned Prior Guidance for Accelerated MRI and qMRI Reconstruction](https://mlsanity.com/paper/2309.00783/) (2023)
- [Harnessing LLMs for API Interactions: A Framework for Classification and Synthetic Data Generation](https://mlsanity.com/paper/2409.11703/) (2024)
- [A Learnable Variational Model for Joint Multimodal MRI Reconstruction and Synthesis](https://mlsanity.com/paper/2204.03804/) (2022)
- [Style Transfer: From Stitching to Neural Networks](https://mlsanity.com/paper/2409.00606/) (2024)
- [Multi-task Magnetic Resonance Imaging Reconstruction using Meta-learning](https://mlsanity.com/paper/2403.19966/) (2024)
- [A Brief Overview of Optimization-Based Algorithms for MRI Reconstruction Using Deep Learning](https://mlsanity.com/paper/2406.02626/) (2024)
- [Enhancing Exchange Rate Forecasting with Explainable Deep Learning Models](https://mlsanity.com/paper/2410.19241/) (2024)
- [Learning to Borrow Features for Improved Detection of Small Objects in Single-Shot Detectors](https://mlsanity.com/paper/2505.00044/) (2025)
- [Deep Unrolled Meta-Learning for Multi-Coil and Multi-Modality MRI with Adaptive Optimization](https://mlsanity.com/paper/2505.11518/) (2025)

## Abstract (arXiv)

Goal: This work aims at developing a novel calibration-free fast parallel MRI (pMRI) reconstruction method incorporate with discrete-time optimal control framework. The reconstruction model is designed to learn a regularization that combines channels and extracts features by leveraging the information sharing among channels of multi-coil images. We propose to recover both magnitude and phase information by taking advantage of structured convolutional networks in image and Fourier spaces. Methods: We develop a novel variational model with a learnable objective function that integrates an adaptive multi-coil image combination operator and effective image regularization in the image and Fourier spaces. We cast the reconstruction network as a structured discrete-time optimal control system, resulting in an optimal control formulation of parameter training where the parameters of the objective function play the role of control variables. We demonstrate that the Lagrangian method for solving the control problem is equivalent to back-propagation, ensuring the local convergence of the training algorithm. Results: We conduct a large number of numerical experiments of the proposed method with comparisons to several state-of-the-art pMRI reconstruction networks on real pMRI datasets. The numerical results demonstrate the promising performance of the proposed method evidently. Conclusion: We conduct a large number of numerical experiments of the proposed method with comparisons to several state-of-the-art pMRI reconstruction networks on real pMRI datasets. The numerical results demonstrate the promising performance of the proposed method evidently. Significance: By learning multi-coil image combination operator and performing regularizations in both image domain and k-space domain, the proposed method achieves a highly efficient image reconstruction network for pMRI.