  Following the success of deep learning in a wide range of applications,
neural network-based machine-learning techniques have received significant
interest for accelerating magnetic resonance imaging (MRI) acquisition and
reconstruction strategies. A number of ideas inspired by deep learning
techniques for computer vision and image processing have been successfully
applied to nonlinear image reconstruction in the spirit of compressed sensing
for accelerated MRI. Given the rapidly growing nature of the field, it is
imperative to consolidate and summarize the large number of deep learning
methods that have been reported in the literature, to obtain a better
understanding of the field in general. This article provides an overview of the
recent developments in neural-network based approaches that have been proposed
specifically for improving parallel imaging. A general background and
introduction to parallel MRI is also given from a classical view of k-space
based reconstruction methods. Image domain based techniques that introduce
improved regularizers are covered along with k-space based methods which focus
on better interpolation strategies using neural networks. While the field is
rapidly evolving with plenty of papers published each year, in this review, we
attempt to cover broad categories of methods that have shown good performance
on publicly available data sets. Limitations and open problems are also
discussed and recent efforts for producing open data sets and benchmarks for
the community are examined.

Image and Video Processing;Computer Vision and Pattern Recognition;Machine Learning