# Learning the Sampling Pattern for MRI

arXiv: https://arxiv.org/abs/1906.08754 · HTML: https://mlsanity.com/paper/1906.08754/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2019.

## Built on by (most cited first, 21 of 21)

- [On Retrospective k-space Subsampling schemes For Deep MRI Reconstruction](https://mlsanity.com/paper/2301.08365/) (2023)
- [Learning Optimal K-space Acquisition and Reconstruction using Physics-Informed Neural Networks](https://mlsanity.com/paper/2204.02480/) (2022)
- [CS4ML: A general framework for active learning with arbitrary data based on Christoffel functions](https://mlsanity.com/paper/2306.00945/) (2023)
- [Deep Learning for Accelerated and Robust MRI Reconstruction: a Review](https://mlsanity.com/paper/2404.15692/) (2024)
- [Analyzing Inexact Hypergradients for Bilevel Learning](https://mlsanity.com/paper/2301.04764/) (2023)
- [Alternating Learning Approach for Variational Networks and Undersampling Pattern in Parallel MRI Applications](https://mlsanity.com/paper/2110.14703/) (2021)
- [On Optimal Regularization Parameters via Bilevel Learning](https://mlsanity.com/paper/2305.18394/) (2023)
- [PUERT: Probabilistic Under-sampling and Explicable Reconstruction Network for CS-MRI](https://mlsanity.com/paper/2204.11189/) (2022)
- [An adaptively inexact first-order method for bilevel optimization with application to hyperparameter learning](https://mlsanity.com/paper/2308.10098/) (2023)
- [JoJoNet: Joint-contrast and Joint-sampling-and-reconstruction Network for Multi-contrast MRI](https://mlsanity.com/paper/2210.12548/) (2022)
- [Single-pass Object-adaptive Data Undersampling and Reconstruction for MRI](https://mlsanity.com/paper/2111.09212/) (2021)
- [Optimizing Sampling Patterns for Compressed Sensing MRI with Diffusion Generative Models](https://mlsanity.com/paper/2306.03284/) (2023)
- [Bilevel Learning with Inexact Stochastic Gradients](https://mlsanity.com/paper/2412.12049/) (2024)
- [Learning to sample in Cartesian MRI](https://mlsanity.com/paper/2312.04327/) (2023)
- [Artificial Intelligence for Neuro MRI Acquisition: A Review](https://mlsanity.com/paper/2406.05982/) (2024)
- [Learning Binary Sampling Patterns for Single-Pixel Imaging using Bilevel Optimisation](https://mlsanity.com/paper/2508.19068/) (2025)
- [LSST: Learned Single-Shot Trajectory and Reconstruction Network for MR Imaging](https://mlsanity.com/paper/2409.07457/) (2024)
- [Bilevel Learning via Inexact Stochastic Gradient Descent](https://mlsanity.com/paper/2511.06774/) (2025)
- [Frequency Error-Guided Under-sampling Optimization for Multi-Contrast MRI Reconstruction](https://mlsanity.com/paper/2601.09316/) (2026)
- [Information-Theoretic Optimization for Task-Adapted Compressed Sensing Magnetic Resonance Imaging](https://mlsanity.com/paper/2604.12709/) (2026)
- [Prior-aware and Context-guided Group Sampling for Active Probabilistic Subsampling](https://mlsanity.com/paper/2607.07083/) (2026)

## Abstract (arXiv)

The discovery of the theory of compressed sensing brought the realisation that many inverse problems can be solved even when measurements are "incomplete". This is particularly interesting in magnetic resonance imaging (MRI), where long acquisition times can limit its use. In this work, we consider the problem of learning a sparse sampling pattern that can be used to optimally balance acquisition time versus quality of the reconstructed image. We use a supervised learning approach, making the assumption that our training data is representative enough of new data acquisitions. We demonstrate that this is indeed the case, even if the training data consists of just 7 training pairs of measurements and ground-truth images; with a training set of brain images of size 192 by 192, for instance, one of the learned patterns samples only 35% of k-space, however results in reconstructions with mean SSIM 0.914 on a test set of similar images. The proposed framework is general enough to learn arbitrary sampling patterns, including common patterns such as Cartesian, spiral and radial sampling.