  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.
