Convolutional Dictionary Learning by End-To-End Training of Iterative Neural Networks

TL;DR

This paper introduces an end-to-end trainable iterative neural network for convolutional dictionary learning, specifically applied to dynamic MRI reconstruction, combining physical models with learned sparsifying transforms.

Contribution

It presents a novel physics-informed INN that jointly learns dictionaries and reconstructs signals without manual regularization tuning, improving interpretability and performance.

Findings

Outperforms traditional model-agnostic methods

Achieves competitive results with deep INNs

Eliminates need for regularization parameter tuning

Abstract

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.