# Learning-Based Compressive MRI

arXiv: https://arxiv.org/abs/1805.01266 · HTML: https://mlsanity.com/paper/1805.01266/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 May 2018.

## Built on by (most cited first, 16 of 16)

- [LAPNet: Non-rigid Registration derived in k-space for Magnetic Resonance Imaging](https://mlsanity.com/paper/2107.09060/) (2021)
- [CS4ML: A general framework for active learning with arbitrary data based on Christoffel functions](https://mlsanity.com/paper/2306.00945/) (2023)
- [Alternating Learning Approach for Variational Networks and Undersampling Pattern in Parallel MRI Applications](https://mlsanity.com/paper/2110.14703/) (2021)
- [LARO: Learned Acquisition and Reconstruction Optimization to accelerate Quantitative Susceptibility Mapping](https://mlsanity.com/paper/2211.00725/) (2022)
- [Model-based Reconstruction with Learning: From Unsupervised to Supervised and Beyond](https://mlsanity.com/paper/2103.14528/) (2021)
- [PUERT: Probabilistic Under-sampling and Explicable Reconstruction Network for CS-MRI](https://mlsanity.com/paper/2204.11189/) (2022)
- [Fast T2w/FLAIR MRI Acquisition by Optimal Sampling of Information Complementary to Pre-acquired T1w MRI](https://mlsanity.com/paper/2111.06400/) (2021)
- [Single-pass Object-adaptive Data Undersampling and Reconstruction for MRI](https://mlsanity.com/paper/2111.09212/) (2021)
- [On Sensitivity and Robustness of Normalization Schemes to Input Distribution Shifts in Automatic MR Image Diagnosis](https://mlsanity.com/paper/2306.13276/) (2023)
- [Learning Binary Sampling Patterns for Single-Pixel Imaging using Bilevel Optimisation](https://mlsanity.com/paper/2508.19068/) (2025)
- [A Weighted Generalized Coherence Approach for Sensing Matrix Design](https://mlsanity.com/paper/2110.02645/) (2021)
- [L2SR: Learning to Sample and Reconstruct for Accelerated MRI via Reinforcement Learning](https://mlsanity.com/paper/2212.02190/) (2022)
- [LSST: Learned Single-Shot Trajectory and Reconstruction Network for MR Imaging](https://mlsanity.com/paper/2409.07457/) (2024)
- [Measurement Geometry and Design for Trustworthy Generative Inverse Problems](https://mlsanity.com/paper/2606.02309/) (2026)
- [One Evaluation, Any Operating Point: Hypernetwork-Amortized MeanFlow for 3D MRI Reconstruction](https://mlsanity.com/paper/2609.31655/) (2026)
- [Active Data Acquisition with Side Information via Discrete Diffusion Priors](https://mlsanity.com/paper/2609.32252/) (2026)

## Abstract (arXiv)

In the area of magnetic resonance imaging (MRI), an extensive range of non-linear reconstruction algorithms have been proposed that can be used with general Fourier subsampling patterns. However, the design of these subsampling patterns has typically been considered in isolation from the reconstruction rule and the anatomy under consideration. In this paper, we propose a learning-based framework for optimizing MRI subsampling patterns for a specific reconstruction rule and anatomy, considering both the noiseless and noisy settings. Our learning algorithm has access to a representative set of training signals, and searches for a sampling pattern that performs well on average for the signals in this set. We present a novel parameter-free greedy mask selection method, and show it to be effective for a variety of reconstruction rules and performance metrics. Moreover we also support our numerical findings by providing a rigorous justification of our framework via statistical learning theory.