  Purpose: Iterative Convolutional Neural Networks (CNNs) which resemble
unrolled learned iterative schemes have shown to consistently deliver
state-of-the-art results for image reconstruction problems across different
imaging modalities. However, because these methodes include the forward model
in the architecture, their applicability is often restricted to either
relatively small reconstruction problems or to problems with operators which
are computationally cheap to compute. As a consequence, they have so far not
been applied to dynamic non-Cartesian multi-coil reconstruction problems.
Methods: In this work, we propose a CNN-architecture for image reconstruction
of accelerated 2D radial cine MRI with multiple receiver coils. The network is
based on a computationally light CNN-component and a subsequent conjugate
gradient (CG) method which can be jointly trained end-to-end using an efficient
training strategy. We investigate the proposed training-strategy and compare
our method to other well-known reconstruction techniques with learned and
non-learned regularization methods. Results: Our proposed method outperforms
all other methods based on non-learned regularization. Further, it performs
similar or better than a CNN-based method employing a 3D U-Net and a method
using adaptive dictionary learning. In addition, we empirically demonstrate
that even by training the network with only iteration, it is possible to
increase the length of the network at test time and further improve the
results. Conclusions: End-to-end training allows to highly reduce the number of
trainable parameters of and stabilize the reconstruction network. Further,
because it is possible to change the length of the network at test time, the
need to find a compromise between the complexity of the CNN-block and the
number of iterations in each CG-block becomes irrelevant.
