  The plug-and-play priors (PnP) and regularization by denoising (RED) methods
have become widely used for solving inverse problems by leveraging pre-trained
deep denoisers as image priors. While the empirical imaging performance and the
theoretical convergence properties of these algorithms have been widely
investigated, their recovery properties have not previously been theoretically
analyzed. We address this gap by showing how to establish theoretical recovery
guarantees for PnP/RED by assuming that the solution of these methods lies near
the fixed-points of a deep neural network. We also present numerical results
comparing the recovery performance of PnP/RED in compressive sensing against
that of recent compressive sensing algorithms based on generative models. Our
numerical results suggest that PnP with a pre-trained artifact removal network
provides significantly better results compared to the existing state-of-the-art
methods.
