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Plug-and-play (PnP) is an optimization framework that integrates pre-trained deep networks (or other nonlinear operators) into ADMM and proximal optimization algorithms with provable convergence. It combines the advantages of deep learning and classic optimization.

PnP lets one use excellent pre-trained networks for tasks where there is not sufficient data for end-to-end training. Although previous PnP work has exhibited great empirical results, theoretical analysis addressing even the basic question of convergence has been insufficient. We establish convergence of PnP-FBS and PnP-ADMM with a constant stepsize (rather than using diminishing stepsizes). The nonlinear operator is required to have a certain Lipschitz condition. To meet this condition, we propose real spectral normalization (realSN), a technique for training deep learning-based denoisers to satisfy the proposed Lipschitz condition.

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