On Plug-and-Play Regularization Using Linear Denoisers

In plug-and-play (PnP) regularization, the knowledge of forward model is combined with a powerful denoiser to obtain state-of-the-art image reconstructions. This typically done by taking proximal algorithm such as FISTA or ADMM, and formally replacing map associated regularizer nonlocal means, BM3D CNN denoiser. Each iterate resulting PnP involves some kind inversion followed denoiser-induced regularization. A natural question in this regard that optimality, namely, do iterations minimize f+g, where f loss function g regularizer? has straightforward solution if can be expressed map, was shown case for class linear symmetric denoisers. However, result excludes kernel denoisers means are inherently non-symmetric. paper, we prove broader (including denoisers) convex g. An algorithmic implication non-symmetric it necessitates appropriate modifications updates ensure convergence minimum f+g. Apart from guarantee, modified algorithms produce good restorations.