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Plug-and-play (PnP) is a non-convex framework that integrates moderndenoising priors, such as BM3D or deep learning-based denoisers, into ADMM orother proximal algorithms. An advantage of PnP is that one can use pre-traineddenoisers when there is not sufficient data for end-to-end training. AlthoughPnP has been recently studied extensively with great empirical success,theoretical analysis addressing even the most basic question of convergence hasbeen insufficient. In this paper, we theoretically establish convergence ofPnP-FBS and PnP-ADMM, without using diminishing stepsizes, under a certainLipschitz condition on the denoisers. We then propose real spectralnormalization, a technique for training deep learning-based denoisers tosatisfy the proposed Lipschitz condition. Finally, we present experimentalresults validating the theory.

Plug-and-Play Methods Provably Converge with Properly Trained Denoisers