Convolutional Analysis Operator Learning by End-to-End Training of Iterative Neural Networks

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.