# On Retrospective k-space Subsampling schemes For Deep MRI Reconstruction arXiv: https://arxiv.org/abs/2301.08365 ยท HTML: https://mlsanity.com/paper/2301.08365/ ## Key facts - Cited by 12 papers in the map (data through 14 Oct 2026). - Builds on 21 of its 61 references that are in the map. - First posted on arXiv 20 Jan 2023. ## Builds on (most cited first, 21 of 21) - [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019) - [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015) - [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018) - [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017) - [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020) - [Deep learning for undersampled MRI reconstruction](https://mlsanity.com/paper/1709.02576/) (2017) - [Reducing Uncertainty in Undersampled MRI Reconstruction with Active Acquisition](https://mlsanity.com/paper/1902.03051/) (2019) - [GrappaNet: Combining Parallel Imaging with Deep Learning for Multi-Coil MRI Reconstruction](https://mlsanity.com/paper/1910.12325/) (2019) - [Experimental design for MRI by greedy policy search](https://mlsanity.com/paper/2010.16262/) (2020) - [Recurrent Variational Network: A Deep Learning Inverse Problem Solver applied to the task of Accelerated MRI Reconstruction](https://mlsanity.com/paper/2111.09639/) (2021) - [Recurrent Inference Machines for Solving Inverse Problems](https://mlsanity.com/paper/1706.04008/) (2017) - [LORAKI: Autocalibrated Recurrent Neural Networks for Autoregressive MRI Reconstruction in k-Space](https://mlsanity.com/paper/1904.09390/) (2019) - [deep-significance - Easy and Meaningful Statistical Significance Testing in the Age of Neural Networks](https://mlsanity.com/paper/2204.06815/) (2022) - [Learning the Sampling Pattern for MRI](https://mlsanity.com/paper/1906.08754/) (2019) - [Multi-Coil MRI Reconstruction Challenge -- Assessing Brain MRI Reconstruction Models and their Generalizability to Varying Coil Configurations](https://mlsanity.com/paper/2011.07952/) (2020) - [On learning adaptive acquisition policies for undersampled multi-coil MRI reconstruction](https://mlsanity.com/paper/2203.16392/) (2022) - [Deep MRI Reconstruction: Unrolled Optimization Algorithms Meet Neural Networks](https://mlsanity.com/paper/1907.11711/) (2019) - [Dual-domain Cascade of U-nets for Multi-channel Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/1911.01458/) (2019) - [Learning Optimal K-space Acquisition and Reconstruction using Physics-Informed Neural Networks](https://mlsanity.com/paper/2204.02480/) (2022) - [Offset Sampling Improves Deep Learning based Accelerated MRI Reconstructions by Exploiting Symmetry](https://mlsanity.com/paper/1912.01101/) (2019) - [Deep MRI Reconstruction with Radial Subsampling](https://mlsanity.com/paper/2108.07619/) (2021) ## Built on by (most cited first, 12 of 12) - [vSHARP: variable Splitting Half-quadratic Admm algorithm for Reconstruction of inverse-Problems](https://mlsanity.com/paper/2309.09954/) (2023) - [Deep Cardiac MRI Reconstruction with ADMM](https://mlsanity.com/paper/2310.06628/) (2023) - [Joint Supervised and Self-supervised Learning for MRI Reconstruction](https://mlsanity.com/paper/2311.15856/) (2023) - [Deep Multi-contrast Cardiac MRI Reconstruction via vSHARP with Auxiliary Refinement Network](https://mlsanity.com/paper/2411.01291/) (2024) - [End-to-end Adaptive Dynamic Subsampling and Reconstruction for Cardiac MRI](https://mlsanity.com/paper/2403.10346/) (2024) - [TEAM PILOT -- Learned Feasible Extendable Set of Dynamic MRI Acquisition Trajectories](https://mlsanity.com/paper/2409.12777/) (2024) - [Active Sampling for MRI-based Sequential Decision Making](https://mlsanity.com/paper/2505.04586/) (2025) - [Multi PILOT: Learned Feasible Multiple Acquisition Trajectories for Dynamic MRI](https://mlsanity.com/paper/2303.07150/) (2023) - [Deep End-to-end Adaptive k-Space Sampling, Reconstruction, and Registration for Dynamic MRI](https://mlsanity.com/paper/2411.18249/) (2024) - [Advancing MRI Reconstruction: A Systematic Review of Deep Learning and Compressed Sensing Integration](https://mlsanity.com/paper/2501.14158/) (2025) - [Distilling Knowledge for Designing Computational Imaging Systems](https://mlsanity.com/paper/2501.17898/) (2025) - [UniFS: Unified Multi-Contrast MRI Reconstruction via Frequency-Spatial Fusion](https://mlsanity.com/paper/2512.05481/) (2025) ## Abstract (arXiv) Acquiring fully-sampled MRI k-space data is time-consuming, and collecting accelerated data can reduce the acquisition time. Employing 2D Cartesian-rectilinear subsampling schemes is a conventional approach for accelerated acquisitions; however, this often results in imprecise reconstructions, even with the use of Deep Learning (DL), especially at high acceleration factors. Non-rectilinear or non-Cartesian trajectories can be implemented in MRI scanners as alternative subsampling options. This work investigates the impact of the k-space subsampling scheme on the quality of reconstructed accelerated MRI measurements produced by trained DL models. The Recurrent Variational Network (RecurrentVarNet) was used as the DL-based MRI-reconstruction architecture. Cartesian, fully-sampled multi-coil k-space measurements from three datasets were retrospectively subsampled with different accelerations using eight distinct subsampling schemes: four Cartesian-rectilinear, two Cartesian non-rectilinear, and two non-Cartesian. Experiments were conducted in two frameworks: scheme-specific, where a distinct model was trained and evaluated for each dataset-subsampling scheme pair, and multi-scheme, where for each dataset a single model was trained on data randomly subsampled by any of the eight schemes and evaluated on data subsampled by all schemes. In both frameworks, RecurrentVarNets trained and evaluated on non-rectilinearly subsampled data demonstrated superior performance, particularly for high accelerations. In the multi-scheme setting, reconstruction performance on rectilinearly subsampled data improved when compared to the scheme-specific experiments. Our findings demonstrate the potential for using DL-based methods, trained on non-rectilinearly subsampled measurements, to optimize scan time and image quality.