  Purpose: To systematically investigate the influence of various data
consistency layers, (semi-)supervised learning and ensembling strategies,
defined in a $\Sigma$-net, for accelerated parallel MR image reconstruction
using deep learning.
  Theory and Methods: MR image reconstruction is formulated as learned unrolled
optimization scheme with a Down-Up network as regularization and varying data
consistency layers. The different architectures are split into sensitivity
networks, which rely on explicit coil sensitivity maps, and parallel coil
networks, which learn the combination of coils implicitly. Different content
and adversarial losses, a semi-supervised fine-tuning scheme and model
ensembling are investigated.
  Results: Evaluated on the fastMRI multicoil validation set, architectures
involving raw k-space data outperform image enhancement methods significantly.
Semi-supervised fine-tuning adapts to new k-space data and provides, together
with reconstructions based on adversarial training, the visually most appealing
results although quantitative quality metrics are reduced. The $\Sigma$-net
ensembles the benefits from different models and achieves similar scores
compared to the single state-of-the-art approaches.
  Conclusion: This work provides an open-source framework to perform a
systematic wide-range comparison of state-of-the-art reconstruction approaches
for parallel MR image reconstruction on the fastMRI knee dataset and explores
the importance of data consistency. A suitable trade-off between perceptual
image quality and quantitative scores are achieved with the ensembled
$\Sigma$-net.
