Robust Deep Equilibrium Paradigms for 3D Hybrid Stack of Stars Reconstruction

Motivation: Exploring the stability of various memory efficient deep equilibrium architectures for non-cartesian stack of stars reconstruction. Goal(s): Implementing memory efficient inversion-based and inversion free deep equilibrium models and assessing performance against unrolled network baselines. Approach: Applying an implicit layer consisting of data-consistency and a 2D-UNet denoiser to find a fixed point and iteratively solving the optimization problem using proximal gradient descent with inversion free and inversion-based equilibrium backpropagation. Compare the efficacy of spectral normalization and Jacobian regularization on stability. Results: The inversion-free deep equilibrium model exhibited performance similar to unrolled networks, achieving a significant 50% reduction in GPU memory usage. Impact: Stable and memory-efficient training advances AI-based reconstructions by enhancing their robustness and efficiency, leading to more accurate diagnoses and treatments, ultimately improving patient care. Moreover, it renders these advanced AI solutions more accessible to resource-constrained systems.