Improved Model based Deep Learning using Monotone Operator Learning (MOL)

TL;DR

This paper introduces a monotone operator learning framework within deep equilibrium models to improve model-based deep learning for image recovery, emphasizing robustness, interpretability, and reduced memory usage.

Contribution

It proposes a novel monotone operator learning approach using DEQ to enhance MoDL algorithms with convergence guarantees and lower memory requirements.

Findings

Reduces memory demand for high-dimensional problems

Provides convergence guarantees and robustness in MRI reconstruction

Demonstrates improved performance in parallel MRI tasks

Abstract

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.