This work proposes a novel optimization framework to learn k-space sampling trajectories using deep learning by considering it an Ordinary Differential Equation (ODE) problem that can be solved using neural ODE. Particularly, 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. 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.
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