Convergent Plug-And-Play Using Contractive Denoisers

Plug-and-Play (PnP) algorithms leverage the power of modern denoisers for image reconstruction. They have been shown to deliver state-of-the-art reconstructions using CNN denoisers. It was established in recent works that convergence of these iterative algorithms can be guaranteed using nonexpansive denoisers. However, integrating nonexpansivity into gradient-based learning is challenging. Existing algorithms for training nonexpansive denoisers often cannot guarantee nonexpansivity or are computationally intensive. The present work is based on the observation that the convergence of PnPFBS and PnP-BBS (PnP based on Forward-Backward and BackwardBackward Splittings) can be guaranteed using contractive denoisers. In this regard, we show that by unfolding FBS iterations applied to wavelet denoising, we can construct contractive image denoisers whose regularization capacity is comparable to CNN denoisers. To the best of knowledge, this is the first work to introduce a simple framework for training denoisers that are provably contractive.