Matching Plug-and-Play Algorithms to the Denoiser

Saurav K Shastri, Rizwan Ahmad, Christopher Metzler, Philip Schniter

Keywords: Inverse problems, plug and play, AMP, GEC, MRI

TL;DR: We design a plug-and-play algorithm using generalized expectation consistent (GEC) approximation that offers predictable error statistics at each iteration, and a deep-net denoiser that can leverage those statistics.

Abstract: To solve inverse problems, plug-and-play (PnP) methods have been developed that replace the proximal step in a convex optimization algorithm with a call to an application-specific denoiser, often implemented using a deep neural network (DNN). Although such methods have been successful, they can be improved. For example, denoisers are usually designed/trained to remove white Gaussian noise, but the denoiser input error in PnP algorithms is usually far from white or Gaussian. Approximate message passing (AMP) methods provide white and Gaussian denoiser input error, but only when the forward operator is a large random matrix. In this work, we propose a PnP algorithm based on generalized expectation consistent (GEC) approximation that offers predictable error statistics at each iteration, as well as a new DNN denoiser that leverages those statistics.