  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.
