demo: learning-based k-space trajectory design

ESMRMB 2025 member session: Self-learning MR

Contact: Felix Glang | Graz University of Technology | glang@tugraz.at

The demo is based on SNOPY (Stochastic optimization framework for 3D NOn-Cartesian samPling trajectorY) by Wang et al. (https://dx.doi.org/10.1002/mrm.29645) from the University of Michigan.
Original code: https://github.com/guanhuaw/SNOPY

Schematic of the approach

Literature

Below is a non-comprehensive overview of some published methods for learning-based design of non-Cartesian trajectories. All of them consider hardware limits, such as gradient amplitudes and slew rates. This means that, rather than learning sampling masks for Cartesian straight-line readouts, they learn true non-Cartesian trajectories.

Method	Year	Code Availability	Comments
SPARKLING	2019	upon request	optimized for CS reco, fixed target sampling density, model-driven, no training data required
3D-SPARKLING	2020	upon request	stack-of-SPARKLING & full 3D
PROJeCTOR	2023	upon request	similar to SPARKLING, data-driven learning of trajectory & reco, projection-based enforcement of hardware constraints
PILOT	2021	https://github.com/tomer196/PILOT	end-to-end learning, option for TSP solver to connect sampling points
3D-FLAT	2020	https://github.com/3d-flat/3dflat	similar to PILOT, 3D
BJORK	2022	https://github.com/guanhuaw/Bjork	B-spline parametrization, analytical NUFFT Jacobian, end-to-end with reco
SNOPY	2023	https://github.com/guanhuaw/SNOPY	similar to BJORK, 3D, PNS penalty, general framework for arbitrary parametrizations

Main objectives

• make efficient use of gradient hardware -> acquisition speed
  • comply with amplitude and slew rate constraints
  • peripheral nerve stimulation
• favourable properties for reconstruction
  • parallel imaging:
    • avoid large gaps between samples (noise amplification -> CAIPI)
    • ...but also not too close (multi-coil correlations -> Poisson disc)
  • compressed sensing:
    • incoherent PSF
    • variable sampling density
  • deep learning:
    • data-driven
    • tailored to specific anatomy?
    • tailored to downstream tasks (e.g. segmentation)?

Challenges

• hardware imperfections (eddy currents, delays, off-resonance, ...)
• many degrees of freedom
  • address by parametrization, e.g. splines
• many local minima
• training data
  • ideally complex multi-coil

Optimization example

Eddy current example