  The concept of sparsity has been extensively applied for regularization in
image reconstruction. Typically, sparsifying transforms are either pre-trained
on ground-truth images or adaptively trained during the reconstruction.
Thereby, learning algorithms are designed to minimize some target function
which encodes the desired properties of the transform. However, this procedure
ignores the subsequently employed reconstruction algorithm as well as the
physical model which is responsible for the image formation process. Iterative
neural networks - which contain the physical model - can overcome these issues.
In this work, we demonstrate how convolutional sparsifying filters can be
efficiently learned by end-to-end training of iterative neural networks. We
evaluated our approach on a non-Cartesian 2D cardiac cine MRI example and show
that the obtained filters are better suitable for the corresponding
reconstruction algorithm than the ones obtained by decoupled pre-training.
