# Learning-based Optimization of the Under-sampling Pattern in MRI

arXiv: https://arxiv.org/abs/1901.01960 · HTML: https://mlsanity.com/paper/1901.01960/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jan 2019.

## Built on by (most cited first, 30 of 33)

- [AI-based Reconstruction for Fast MRI -- A Systematic Review and Meta-analysis](https://mlsanity.com/paper/2112.12744/) (2021)
- [On learning adaptive acquisition policies for undersampled multi-coil MRI reconstruction](https://mlsanity.com/paper/2203.16392/) (2022)
- [End-to-End Sequential Sampling and Reconstruction for MRI](https://mlsanity.com/paper/2105.06460/) (2021)
- [A review and experimental evaluation of deep learning methods for MRI reconstruction](https://mlsanity.com/paper/2109.08618/) (2021)
- [Probabilistic Bayesian optimal experimental design using conditional normalizing flows](https://mlsanity.com/paper/2402.18337/) (2024)
- [Optimal MRI Undersampling Patterns for Ultimate Benefit of Medical Vision Tasks](https://mlsanity.com/paper/2108.04914/) (2021)
- [Adaptive Sampling of k-Space in Magnetic Resonance for Rapid Pathology Prediction](https://mlsanity.com/paper/2406.04318/) (2024)
- [Alternating Learning Approach for Variational Networks and Undersampling Pattern in Parallel MRI Applications](https://mlsanity.com/paper/2110.14703/) (2021)
- [One Network to Solve Them All: A Sequential Multi-Task Joint Learning Network Framework for MR Imaging Pipeline](https://mlsanity.com/paper/2105.06653/) (2021)
- [PUERT: Probabilistic Under-sampling and Explicable Reconstruction Network for CS-MRI](https://mlsanity.com/paper/2204.11189/) (2022)
- [ReconResNet: Regularised Residual Learning for MR Image Reconstruction of Undersampled Cartesian and Radial Data](https://mlsanity.com/paper/2103.09203/) (2021)
- [JoJoNet: Joint-contrast and Joint-sampling-and-reconstruction Network for Multi-contrast MRI](https://mlsanity.com/paper/2210.12548/) (2022)
- [On the Feasibility of Machine Learning Augmented Magnetic Resonance for Point-of-Care Identification of Disease](https://mlsanity.com/paper/2301.11962/) (2023)
- [Learning Task-Specific Strategies for Accelerated MRI](https://mlsanity.com/paper/2304.12507/) (2023)
- [Fast T2w/FLAIR MRI Acquisition by Optimal Sampling of Information Complementary to Pre-acquired T1w MRI](https://mlsanity.com/paper/2111.06400/) (2021)
- [Constrained Probabilistic Mask Learning for Task-specific Undersampled MRI Reconstruction](https://mlsanity.com/paper/2305.16376/) (2023)
- [End-to-end Adaptive Dynamic Subsampling and Reconstruction for Cardiac MRI](https://mlsanity.com/paper/2403.10346/) (2024)
- [Deep Simultaneous Optimisation of Sampling and Reconstruction for Multi-contrast MRI](https://mlsanity.com/paper/2103.16744/) (2021)
- [Active Phase-Encode Selection for Slice-Specific Fast MR Scanning Using a Transformer-Based Deep Reinforcement Learning Framework](https://mlsanity.com/paper/2203.05756/) (2022)
- [Optimal OnTheFly Feedback Control of Event Sensors](https://mlsanity.com/paper/2408.12976/) (2024)
- [SIREM: Speech-Informed MRI Reconstruction with Learned Sampling](https://mlsanity.com/paper/2605.18221/) (2026)
- [Motion Artifact Reduction in Quantitative Susceptibility Mapping using Deep Neural Network](https://mlsanity.com/paper/2105.01746/) (2021)
- [Benchmarking learned non-Cartesian k-space trajectories and reconstruction networks](https://mlsanity.com/paper/2201.11356/) (2022)
- [Gradient-Based Learning of Discrete Structured Measurement Operators for Signal Recovery](https://mlsanity.com/paper/2202.03391/) (2022)
- [FReSCO: Flow Reconstruction and Segmentation for low latency Cardiac Output monitoring using deep artifact suppression and segmentation](https://mlsanity.com/paper/2203.13729/) (2022)
- [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)
- [Deep End-to-end Adaptive k-Space Sampling, Reconstruction, and Registration for Dynamic MRI](https://mlsanity.com/paper/2411.18249/) (2024)
- [Predicting before Reconstruction: A generative prior framework for MRI acceleration](https://mlsanity.com/paper/2510.19472/) (2025)
- [Anatomical Token Uncertainty for Transformer-Guided Active MRI Acquisition](https://mlsanity.com/paper/2603.21806/) (2026)

## Abstract (arXiv)

Acquisition of Magnetic Resonance Imaging (MRI) scans can be accelerated by under-sampling in k-space (i.e., the Fourier domain). In this paper, we consider the problem of optimizing the sub-sampling pattern in a data-driven fashion. Since the reconstruction model's performance depends on the sub-sampling pattern, we combine the two problems. For a given sparsity constraint, our method optimizes the sub-sampling pattern and reconstruction model, using an end-to-end learning strategy. Our algorithm learns from full-resolution data that are under-sampled retrospectively, yielding a sub-sampling pattern and reconstruction model that are customized to the type of images represented in the training data. The proposed method, which we call LOUPE (Learning-based Optimization of the Under-sampling PattErn), was implemented by modifying a U-Net, a widely-used convolutional neural network architecture, that we append with the forward model that encodes the under-sampling process. Our experiments with T1-weighted structural brain MRI scans show that the optimized sub-sampling pattern can yield significantly more accurate reconstructions compared to standard random uniform, variable density or equispaced under-sampling schemes. The code is made available at: https://github.com/cagladbahadir/LOUPE .