  To solve inverse problems, plug-and-play (PnP) methods 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 yield accurate solutions, 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 sufficiently random. In this
work, for Fourier-based forward operators, we propose a PnP algorithm based on
generalized expectation-consistent (GEC) approximation -- a close cousin of AMP
-- that offers predictable error statistics at each iteration, as well as a new
DNN denoiser that leverages those statistics. We apply our approach to magnetic
resonance (MR) image recovery and demonstrate its advantages over existing PnP
and AMP methods.
