  In this work, we propose a deep learning approach for parallel magnetic
resonance imaging (MRI) reconstruction, termed a variable splitting network
(VS-Net), for an efficient, high-quality reconstruction of undersampled
multi-coil MR data. We formulate the generalized parallel compressed sensing
reconstruction as an energy minimization problem, for which a variable
splitting optimization method is derived. Based on this formulation we propose
a novel, end-to-end trainable deep neural network architecture by unrolling the
resulting iterative process of such variable splitting scheme. VS-Net is
evaluated on complex valued multi-coil knee images for 4-fold and 6-fold
acceleration factors. We show that VS-Net outperforms state-of-the-art deep
learning reconstruction algorithms, in terms of reconstruction accuracy and
perceptual quality. Our code is publicly available at
https://github.com/j-duan/VS-Net.
