# B-spline Parameterized Joint Optimization of Reconstruction and K-space Trajectories (BJORK) for Accelerated 2D MRI

arXiv: https://arxiv.org/abs/2101.11369 · HTML: https://mlsanity.com/paper/2101.11369/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2021.

## Built on by (most cited first, 29 of 29)

- [Physics-Driven Deep Learning for Computational Magnetic Resonance Imaging](https://mlsanity.com/paper/2203.12215/) (2022)
- [On learning adaptive acquisition policies for undersampled multi-coil MRI reconstruction](https://mlsanity.com/paper/2203.16392/) (2022)
- [Learning Fourier-Constrained Diffusion Bridges for MRI Reconstruction](https://mlsanity.com/paper/2308.01096/) (2023)
- [End-to-End Sequential Sampling and Reconstruction for MRI](https://mlsanity.com/paper/2105.06460/) (2021)
- [Physics-Driven Autoregressive State Space Models for Medical Image Reconstruction](https://mlsanity.com/paper/2412.09331/) (2024)
- [Optimal MRI Undersampling Patterns for Ultimate Benefit of Medical Vision Tasks](https://mlsanity.com/paper/2108.04914/) (2021)
- [Alternating Learning Approach for Variational Networks and Undersampling Pattern in Parallel MRI Applications](https://mlsanity.com/paper/2110.14703/) (2021)
- [Towards Ultrafast MRI via Extreme k-Space Undersampling and Superresolution](https://mlsanity.com/paper/2103.02940/) (2021)
- [Training Adaptive Reconstruction Networks for Blind Inverse Problems](https://mlsanity.com/paper/2202.11342/) (2022)
- [HyperSLICE: HyperBand optimized Spiral for Low-latency Interactive Cardiac Examination](https://mlsanity.com/paper/2302.02688/) (2023)
- [Learning Task-Specific Strategies for Accelerated MRI](https://mlsanity.com/paper/2304.12507/) (2023)
- [Single-pass Object-adaptive Data Undersampling and Reconstruction for MRI](https://mlsanity.com/paper/2111.09212/) (2021)
- [Constrained Probabilistic Mask Learning for Task-specific Undersampled MRI Reconstruction](https://mlsanity.com/paper/2305.16376/) (2023)
- [Optimizing Sampling Patterns for Compressed Sensing MRI with Diffusion Generative Models](https://mlsanity.com/paper/2306.03284/) (2023)
- [Adaptive Selection of Sampling-Reconstruction in Fourier Compressed Sensing](https://mlsanity.com/paper/2409.11738/) (2024)
- [TEAM PILOT -- Learned Feasible Extendable Set of Dynamic MRI Acquisition Trajectories](https://mlsanity.com/paper/2409.12777/) (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)
- [Optimal OnTheFly Feedback Control of Event Sensors](https://mlsanity.com/paper/2408.12976/) (2024)
- [A Comprehensive Survey on Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/2503.07097/) (2025)
- [Active Sampling for MRI-based Sequential Decision Making](https://mlsanity.com/paper/2505.04586/) (2025)
- [On The Role of K-Space Acquisition in MRI Reconstruction Domain-Generalization](https://mlsanity.com/paper/2512.06530/) (2025)
- [Benchmarking learned non-Cartesian k-space trajectories and reconstruction networks](https://mlsanity.com/paper/2201.11356/) (2022)
- [L2SR: Learning to Sample and Reconstruct for Accelerated MRI via Reinforcement Learning](https://mlsanity.com/paper/2212.02190/) (2022)
- [Multi PILOT: Learned Feasible Multiple Acquisition Trajectories for Dynamic MRI](https://mlsanity.com/paper/2303.07150/) (2023)
- [LSST: Learned Single-Shot Trajectory and Reconstruction Network for MR Imaging](https://mlsanity.com/paper/2409.07457/) (2024)
- [T1-PILOT: Optimized Trajectories for T1 Mapping Acceleration](https://mlsanity.com/paper/2502.20333/) (2025)
- [Sequence Search: Automated Sequence Design using Neural Architecture Search](https://mlsanity.com/paper/2604.14788/) (2026)
- [NexOP: Joint Optimization of NEX-Aware k-space Sampling and Image Reconstruction for Low-Field MRI](https://mlsanity.com/paper/2605.11583/) (2026)

## Abstract (arXiv)

Optimizing k-space sampling trajectories is a promising yet challenging topic for fast magnetic resonance imaging (MRI). This work proposes to optimize a reconstruction method and sampling trajectories jointly concerning image reconstruction quality in a supervised learning manner. We parameterize trajectories with quadratic B-spline kernels to reduce the number of parameters and apply multi-scale optimization, which may help to avoid sub-optimal local minima. The algorithm includes an efficient non-Cartesian unrolled neural network-based reconstruction and an accurate approximation for backpropagation through the non-uniform fast Fourier transform (NUFFT) operator to accurately reconstruct and back-propagate multi-coil non-Cartesian data. Penalties on slew rate and gradient amplitude enforce hardware constraints. Sampling and reconstruction are trained jointly using large public datasets. To correct for possible eddy-current effects introduced by the curved trajectory, we use a pencil-beam trajectory mapping technique. In both simulations and in-vivo experiments, the learned trajectory demonstrates significantly improved image quality compared to previous model-based and learning-based trajectory optimization methods for 10 times acceleration factors. Though trained with neural network-based reconstruction, the proposed trajectory also leads to improved image quality with compressed sensing-based reconstruction.