  Following the success of deep learning in a wide range of applications,
neural network-based machine learning techniques have received interest as a
means of accelerating magnetic resonance imaging (MRI). A number of ideas
inspired by deep learning techniques from computer vision and image processing
have been successfully applied to non-linear image reconstruction in the spirit
of compressed sensing for both low dose computed tomography and accelerated
MRI. The additional integration of multi-coil information to recover missing
k-space lines in the MRI reconstruction process, is still studied less
frequently, even though it is the de-facto standard for currently used
accelerated MR acquisitions. This manuscript provides an overview of the recent
machine learning approaches that have been proposed specifically for improving
parallel imaging. A general background introduction to parallel MRI is given
that is structured around the classical view of image space and k-space based
methods. Both linear and non-linear methods are covered, followed by a
discussion of recent efforts to further improve parallel imaging using machine
learning, and specifically using artificial neural networks. Image-domain based
techniques that introduce improved regularizers are covered as well as k-space
based methods, where the focus is on better interpolation strategies using
neural networks. Issues and open problems are discussed as well as recent
efforts for producing open datasets and benchmarks for the community.
