Online Deep Equilibrium Learning for Regularization by Denoising
This work addresses a computational bottleneck for researchers and practitioners in imaging, making DEQ-based methods more practical, though it is incremental as it builds on existing DEQ and PnP/RED frameworks.
The paper tackles the computational inefficiency of Deep Equilibrium Models (DEQ) in Plug-and-Play Priors (PnP) and Regularization by Denoising (RED) for imaging inverse problems by proposing ODER, a strategy using stochastic approximations to reduce training and testing complexity, with numerical results showing potential improvements in three imaging applications.
Plug-and-Play Priors (PnP) and Regularization by Denoising (RED) are widely-used frameworks for solving imaging inverse problems by computing fixed-points of operators combining physical measurement models and learned image priors. While traditional PnP/RED formulations have focused on priors specified using image denoisers, there is a growing interest in learning PnP/RED priors that are end-to-end optimal. The recent Deep Equilibrium Models (DEQ) framework has enabled memory-efficient end-to-end learning of PnP/RED priors by implicitly differentiating through the fixed-point equations without storing intermediate activation values. However, the dependence of the computational/memory complexity of the measurement models in PnP/RED on the total number of measurements leaves DEQ impractical for many imaging applications. We propose ODER as a new strategy for improving the efficiency of DEQ through stochastic approximations of the measurement models. We theoretically analyze ODER giving insights into its convergence and ability to approximate the traditional DEQ approach. Our numerical results suggest the potential improvements in training/testing complexity due to ODER on three distinct imaging applications.