Improved Model based Deep Learning using Monotone Operator Learning (MOL)
This work addresses memory and robustness issues in model-based deep learning for image recovery, particularly in medical imaging like MRI, offering an incremental improvement over existing unrolled methods.
The authors tackled the challenges of high memory cost, lack of robustness guarantees, and low interpretability in model-based deep learning for image recovery by introducing a monotone operator learning framework using deep equilibrium and Jacobian iterations, which significantly reduces memory demand and provides guaranteed convergence and robustness, demonstrated in parallel MRI applications.
Model-based deep learning (MoDL) algorithms that rely on unrolling are emerging as powerful tools for image recovery. In this work, we introduce a novel monotone operator learning framework to overcome some of the challenges associated with current unrolled frameworks, including high memory cost, lack of guarantees on robustness to perturbations, and low interpretability. Unlike current unrolled architectures that use finite number of iterations, we use the deep equilibrium (DEQ) framework to iterate the algorithm to convergence and to evaluate the gradient of the convolutional neural network blocks using Jacobian iterations. This approach significantly reduces the memory demand, facilitating the extension of MoDL algorithms to high dimensional problems. We constrain the CNN to be a monotone operator, which allows us to introduce algorithms with guaranteed convergence properties and robustness guarantees. We demonstrate the utility of the proposed scheme in the context of parallel MRI.