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  1. Optimization-based k-space sampling pattern design often involves the Jacobian matrix of non-uniform fast Fourier transform (NUFFT) operations. Previous works relying on auto-differentiation can be time-consuming and less accurate. This work proposes an approximation method using the relationship between exact non-uniform DFT (NDFT) and NUFFT, demonstrating improved results for the sampling pattern optimization problem.
  2. The proposed approach, BJORK, provides a robust and generalizable workflow to jointly optimize non-Cartesian sampling patters and a physics-informed reconstruction. Several approaches, including re-parameterization of trajectories, multi-level optimization, and non-Cartesian unrolled neural networks, are introduced to improve training effect and avoid sub-optimal local minima. The invivo experiments show that the networks and trajectories learned on simulation dataset are transferable to the real acquisition even with different parameter-weighted MRI contrasts and noise-levels, and demonstrate improved image quality compared with previous learning-based and model-based trajectory optimization methods.