Monotone Operator Learning: a robust and memory-efficient physics-guided deep learning framework

MRI has been revolutionized by compressed sensing algorithms, which offer guaranteed uniqueness, convergence, and stability. In the recent years, model-based deep learning methods have been emerging as more powerful alternatives for image recovery. The main focus of this paper is to introduce a model based algorithm with similar theoretical guarantees as CS methods. The proposed deep equilibrium formulation is significantly more memory-efficient than unrolled methods, which allows us to apply it to 3D or 2D+time problems that current unrolled algorithms cannot handle. Our results also show that the approach is more robust to input perturbations than current unrolled methods.