Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Condition
This addresses the theoretical gap in understanding recovery properties for widely used PnP/RED methods in imaging, which is incremental as it builds on existing empirical work.
The paper tackles the lack of theoretical recovery guarantees for plug-and-play priors (PnP) and regularization by denoising (RED) methods in inverse problems by showing how to establish such guarantees assuming solutions lie near fixed-points of a deep neural network, and numerical results in compressive sensing indicate PnP with a pre-trained artifact removal network provides significantly better results than state-of-the-art methods.
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.