  Magnetic Resonance Image (MRI) acquisition is an inherently slow process
which has spurred the development of two different acceleration methods:
acquiring multiple correlated samples simultaneously (parallel imaging) and
acquiring fewer samples than necessary for traditional signal processing
methods (compressed sensing). Both methods provide complementary approaches to
accelerating the speed of MRI acquisition. In this paper, we present a novel
method to integrate traditional parallel imaging methods into deep neural
networks that is able to generate high quality reconstructions even for high
acceleration factors. The proposed method, called GrappaNet, performs
progressive reconstruction by first mapping the reconstruction problem to a
simpler one that can be solved by a traditional parallel imaging methods using
a neural network, followed by an application of a parallel imaging method, and
finally fine-tuning the output with another neural network. The entire network
can be trained end-to-end. We present experimental results on the recently
released fastMRI dataset and show that GrappaNet can generate higher quality
reconstructions than competing methods for both $4\times$ and $8\times$
acceleration.
