# Learning Optimal K-space Acquisition and Reconstruction using Physics-Informed Neural Networks

arXiv: https://arxiv.org/abs/2204.02480 · HTML: https://mlsanity.com/paper/2204.02480/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 58 references that are in the map.
- First posted on arXiv 5 Apr 2022.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [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)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [Compressed Sensing MRI Reconstruction using a Generative Adversarial Network with a Cyclic Loss](https://mlsanity.com/paper/1709.00753/) (2017)
- [Reducing Uncertainty in Undersampled MRI Reconstruction with Active Acquisition](https://mlsanity.com/paper/1902.03051/) (2019)
- [Experimental design for MRI by greedy policy search](https://mlsanity.com/paper/2010.16262/) (2020)
- [Deep Learning with Domain Adaptation for Accelerated Projection-Reconstruction MR](https://mlsanity.com/paper/1703.01135/) (2017)
- [PILOT: Physics-Informed Learned Optimized Trajectories for Accelerated MRI](https://mlsanity.com/paper/1909.05773/) (2019)
- [Learning the Sampling Pattern for MRI](https://mlsanity.com/paper/1906.08754/) (2019)
- [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)

## Built on by (most cited first, 11 of 11)

- [Large language models in healthcare and medical domain: A review](https://mlsanity.com/paper/2401.06775/) (2023)
- [Evaluating General Purpose Vision Foundation Models for Medical Image Analysis: An Experimental Study of DINOv2 on Radiology Benchmarks](https://mlsanity.com/paper/2312.02366/) (2023)
- [On Retrospective k-space Subsampling schemes For Deep MRI Reconstruction](https://mlsanity.com/paper/2301.08365/) (2023)
- [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)
- [The Role of Language Models in Modern Healthcare: A Comprehensive Review](https://mlsanity.com/paper/2409.16860/) (2024)
- [Efficient Noise Calculation in Deep Learning-based MRI Reconstructions](https://mlsanity.com/paper/2505.02007/) (2025)
- [On The Role of K-Space Acquisition in MRI Reconstruction Domain-Generalization](https://mlsanity.com/paper/2512.06530/) (2025)
- [Physical foundations for trustworthy medical imaging: a review for artificial intelligence researchers](https://mlsanity.com/paper/2505.02843/) (2025)
- [Sequence Search: Automated Sequence Design using Neural Architecture Search](https://mlsanity.com/paper/2604.14788/) (2026)
- [Frequency-Hierarchical Active k-Space Sampling for Diagnostic MRI](https://mlsanity.com/paper/2607.19779/) (2026)

## Abstract (arXiv)

The inherent slow imaging speed of Magnetic Resonance Image (MRI) has spurred the development of various acceleration methods, typically through heuristically undersampling the MRI measurement domain known as k-space. Recently, deep neural networks have been applied to reconstruct undersampled k-space data and have shown improved reconstruction performance. While most of these methods focus on designing novel reconstruction networks or new training strategies for a given undersampling pattern, e.g., Cartesian undersampling or Non-Cartesian sampling, to date, there is limited research aiming to learn and optimize k-space sampling strategies using deep neural networks. This work proposes a novel optimization framework to learn k-space sampling trajectories by considering it as an Ordinary Differential Equation (ODE) problem that can be solved using neural ODE. In particular, the sampling of k-space data is framed as a dynamic system, in which neural ODE is formulated to approximate the system with additional constraints on MRI physics. In addition, we have also demonstrated that trajectory optimization and image reconstruction can be learned collaboratively for improved imaging efficiency and reconstruction performance. Experiments were conducted on different in-vivo datasets (e.g., brain and knee images) acquired with different sequences. Initial results have shown that our proposed method can generate better image quality in accelerated MRI than conventional undersampling schemes in Cartesian and Non-Cartesian acquisitions.