Memory-efficient and robust model-based deep learning using non-montone monotone operator learning (MnM-MOL)

Motivation: The high memory demand of model-based deep learning algorithms restricts their application in large-scale (eg., 3D/4D) applications. Moreover, their robustness to input perturbations is not well-studied. Goal(s): To realize a memory efficient MoDL framework with similar theoretical guarantees as compressed sensing methods, while offering state-of-the-art performance. Approach: We introduce a memory-efficient deep equilibrium framework with theoretical guarantees on uniqueness, convergence, and robustness. Results: The proposed scheme offers comparable performance to state of the art methods, while being 10 times more memory-efficient. Additionally, the proposed scheme is significantly more robust to Gaussian and adversarial input perturbations. Impact: The proposed approach results in greater than 10x reduction in memory demand, which enables the application of MoDL algorithms in large-scale (3D/4D) applications. The theoretically guaranteed robustness of the proposed algorithm reduces the error amplification in highly under-sampled settings.