i-DEQ: A stable inertial deep equilibrium model for image restoration

Accelerated MRI reconstruction is a classical inverse problem. However, designing reconstruction models that are computationally efficient, stable, and provide convergence guarantees remains an open challenge. Deep Equilibrium Models (DEQs) offer a promising framework by casting reconstruction as a fixed-point problem, where problem-adapted regularizations can be learned directly from data. However, standard DEQs often suffer from high computational costs and training instability. We propose an inertial DEQ model, \textbf{i-DEQ}, that learns an explicit nonconvex regularization and incorporates momentum into the fixed-point iterations. i-DEQ achieves accelerated convergence while retaining convergence guarantees. Applied to accelerated MRI reconstruction, i-DEQ achieves state-of-the-art performance.