Generative Plug and Play: Posterior Sampling for Inverse Problems
Charles A. Bouman Gregery T. Buzzard
Over the past decade, Plug-and-Play (PnP) has become a popular method for
reconstructing images using a modular framework consisting of a forward and
prior model. The great strength of PnP is that an image denoiser can be used as
a prior model while the forward model can be implemented using more traditional
physics-based approaches. However, a limitation of PnP is that it reconstructs
only a single deterministic image.
  In this paper, we introduce Generative Plug-and-Play (GPnP), a generalization
of PnP to sample from the posterior distribution. As with PnP, GPnP has a
modular framework using a physics-based forward model and an image denoising
prior model. However, in GPnP these models are extended to become proximal
generators, which sample from associated distributions. GPnP applies these
proximal generators in alternation to produce samples from the posterior. We
present experimental simulations using the well-known BM3D denoiser. Our
results demonstrate that the GPnP method is robust, easy to implement, and
produces intuitively reasonable samples from the posterior for sparse
interpolation and tomographic reconstruction. Code to accompany this paper is
available at https://github.com/gbuzzard/generative-pnp-allerton .