Convolutional Dictionary Learning by End-To-End Training of Iterative Neural Networks
This work addresses the challenge of physics-informed dictionary learning for medical imaging reconstruction, offering an incremental improvement in interpretability and parameter-free training over existing methods.
The authors tackled the problem of training sparsifying dictionaries in conjunction with a physical model for image reconstruction, specifically in dynamic MRI, by proposing an iterative neural network (INN) for supervised convolutional dictionary learning. They showed that this approach improves over conventional model-agnostic methods and yields competitive results compared to a deep INN, while eliminating the need for regularization parameter tuning and maintaining interpretability.
Sparsity-based methods have a long history in the field of signal processing and have been successfully applied to various image reconstruction problems. The involved sparsifying transformations or dictionaries are typically either pre-trained using a model which reflects the assumed properties of the signals or adaptively learned during the reconstruction - yielding so-called blind Compressed Sensing approaches. However, by doing so, the transforms are never explicitly trained in conjunction with the physical model which generates the signals. In addition, properly choosing the involved regularization parameters remains a challenging task. Another recently emerged training-paradigm for regularization methods is to use iterative neural networks (INNs) - also known as unrolled networks - which contain the physical model. In this work, we construct an INN which can be used as a supervised and physics-informed online convolutional dictionary learning algorithm. We evaluated the proposed approach by applying it to a realistic large-scale dynamic MR reconstruction problem and compared it to several other recently published works. We show that the proposed INN improves over two conventional model-agnostic training methods and yields competitive results also compared to a deep INN. Further, it does not require to choose the regularization parameters and - in contrast to deep INNs - each network component is entirely interpretable.