  Purpose: To allow fast and high-quality reconstruction of clinical
accelerated multi-coil MR data by learning a variational network that combines
the mathematical structure of variational models with deep learning.
  Theory and Methods: Generalized compressed sensing reconstruction formulated
as a variational model is embedded in an unrolled gradient descent scheme. All
parameters of this formulation, including the prior model defined by filter
kernels and activation functions as well as the data term weights, are learned
during an offline training procedure. The learned model can then be applied
online to previously unseen data.
  Results: The variational network approach is evaluated on a clinical knee
imaging protocol. The variational network reconstructions outperform standard
reconstruction algorithms in terms of image quality and residual artifacts for
all tested acceleration factors and sampling patterns.
  Conclusion: Variational network reconstructions preserve the natural
appearance of MR images as well as pathologies that were not included in the
training data set. Due to its high computational performance, i.e.,
reconstruction time of 193 ms on a single graphics card, and the omission of
parameter tuning once the network is trained, this new approach to image
reconstruction can easily be integrated into clinical workflow.
