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Improved Model based Deep Learning using Monotone Operator Learning (MOL)
Preprint   Open access

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

Aniket Pramanik and Mathews Jacob
ArXiv.org
11/22/2021
DOI: 10.48550/arXiv.2111.11380
url
https://arxiv.org/abs/2111.11380View
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

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.

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