  The annihilating filter-based low-rank Hankel 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.
The success of ALOHA is due to the concise signal representation in the k-space
domain thanks to the duality between structured low-rankness in the k-space
domain and the image domain sparsity. Inspired by the recent mathematical
discovery that links convolutional 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 regridding layer. Extensive numerical experiments show that the
proposed deep learning method consistently outperforms the existing
image-domain deep learning approaches.
