Learning Optimal K-Space Acquisition and Reconstruction Using Physics-Informed Neural Networks

Wei Peng, Li Feng, Guoying Zhao, Fang Liu; Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022, pp. 20794-20803

The inherent slow imaging speed of Magnetic Resonance Image (MRI) has spurred the development of various acceleration methods, typically through heuristically undersampling of the associated measurement domain known as k-space. Recently, deep neural networks have been applied to reconstruct undersampled k-space and shown improved reconstruction performance. While most methods focus on designing novel reconstruction networks or new training strategies for a given undersampling pattern, e.g., random Cartesian undersampling or standard non-Cartesian sampling, to date, there is limited research that aims to learn and optimize k-space sampling strategies using deep neural networks. In this work, we propose a novel framework to learn optimized k-space sampling trajectories using deep learning 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 the control points serve as an initial state and a physical-conditioned neural ODE is formulated to approximate the system. Moreover, we also enforce additional constraints on gradient slew rate and amplitude in trajectory learning, so that severe gradient-indued artifacts can be minimized. Furthermore, we have also demonstrated that sampling trajectory optimization and MRI reconstruction can be jointly trained, such that the optimized trajectory is task-oriented and can enhance overall image reconstruction performance. Experiments were conducted on different in-vivo dataset (e.g., Brain and Knee) with different contrast. Initial results have shown that our proposed method is able to generate better image quality in accelerated MRI compared to conventional undersampling schemes in both Cartesian and non-Cartesian acquisitions.