# Alternating Learning Approach for Variational Networks and Undersampling Pattern in Parallel MRI Applications

arXiv: https://arxiv.org/abs/2110.14703 · HTML: https://mlsanity.com/paper/2110.14703/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 60 references that are in the map.
- First posted on arXiv 27 Oct 2021.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Deep Learning Methods for Parallel Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/1904.01112/) (2019)
- [Learning-based Optimization of the Under-sampling Pattern in MRI](https://mlsanity.com/paper/1901.01960/) (2019)
- [B-spline Parameterized Joint Optimization of Reconstruction and K-space Trajectories (BJORK) for Accelerated 2D MRI](https://mlsanity.com/paper/2101.11369/) (2021)
- [PILOT: Physics-Informed Learned Optimized Trajectories for Accelerated MRI](https://mlsanity.com/paper/1909.05773/) (2019)
- [Extending LOUPE for K-space Under-sampling Pattern Optimization in Multi-coil MRI](https://mlsanity.com/paper/2007.14450/) (2020)
- [Learning the Sampling Pattern for MRI](https://mlsanity.com/paper/1906.08754/) (2019)
- [Learning-Based Compressive MRI](https://mlsanity.com/paper/1805.01266/) (2018)
- [OEDIPUS: An Experiment Design Framework for Sparsity-Constrained MRI](https://mlsanity.com/paper/1805.00524/) (2018)
- [Scalable Learning-Based Sampling Optimization for Compressive Dynamic MRI](https://mlsanity.com/paper/1902.00386/) (2019)
- [Fast Variable Density Poisson-Disc Sample Generation with Directional Variation](https://mlsanity.com/paper/2004.06789/) (2020)

## Built on by (most cited first, 6 of 6)

- [On learning adaptive acquisition policies for undersampled multi-coil MRI reconstruction](https://mlsanity.com/paper/2203.16392/) (2022)
- [PUERT: Probabilistic Under-sampling and Explicable Reconstruction Network for CS-MRI](https://mlsanity.com/paper/2204.11189/) (2022)
- [Learning Task-Specific Strategies for Accelerated MRI](https://mlsanity.com/paper/2304.12507/) (2023)
- [Optimizing Sampling Patterns for Compressed Sensing MRI with Diffusion Generative Models](https://mlsanity.com/paper/2306.03284/) (2023)
- [MASC: Metal-Aware Sampling and Correction via Reinforcement Learning for Accelerated MRI](https://mlsanity.com/paper/2602.00348/) (2026)
- [Evaluating the Safety of Deep Learning-Based Brain MRI Reconstruction](https://mlsanity.com/paper/2608.28714/) (2026)

## Abstract (arXiv)

Purpose: To propose an alternating learning approach to learn the sampling pattern (SP) and the parameters of variational networks (VN) in accelerated parallel magnetic resonance imaging (MRI). Methods: The approach alternates between improving the SP, using bias-accelerated subset selection, and improving parameters of the VN, using ADAM with monotonicity verification. The algorithm learns an effective pair: an SP that captures fewer k-space samples generating undersampling artifacts that are removed by the VN reconstruction. The proposed approach was tested for stability and convergence, considering different initial SPs. The quality of the VNs and SPs was compared against other approaches, including joint learning methods and VN learning with fixed variable density Poisson-disc SPs, using two different datasets and different acceleration factors (AF). Results: The root mean squared error (RMSE) improvements ranged from 14.9% to 51.2% considering AF from 2 to 20 in the tested brain and knee joint datasets when compared to the other approaches. The proposed approach has shown stable convergence, obtaining similar SPs with the same RMSE under different initial conditions. Conclusion: The proposed approach was stable and learned effective SPs with the corresponding VN parameters that produce images with better quality than other approaches, improving accelerated parallel MRI applications.