k-Space Deep Learning for Accelerated MRI

The annihilating filter-based low-rank Hanel matrix approach (ALOHA) is one of the state-of-the-art compressed sensing approaches that directly interpolates the missing k-space data using low-rank Hankel matrix completion. Inspired by the recent mathematical discovery that links deep neural networks to Hankel matrix decomposition using data-driven framelet basis, here we propose a fully data-driven deep learning algorithm for k-space interpolation. Our network can be also easily applied to non-Cartesian k-space trajectories by simply adding an additional re-gridding layer. Extensive numerical experiments show that the proposed deep learning method significantly outperforms the existing image-domain deep learning approaches.