Parameter-free Plug-and-Play ADMM for image restoration

Plug-and-Play ADMM is a recently developed variation of the classical ADMM algorithm that replaces one of the subproblems using an off-the-shelf image denoiser. Despite its apparently ad-hoc nature, Plug-and-Play ADMM produces surprisingly good image recovery results. However, since in Plug-and-Play ADMM the denoiser is treated as a black-box, behavior of the overall algorithm is largely unknown. In particular, the internal parameter that controls the rate of convergence of the algorithm has to be adjusted by the user, and a bad choice of the parameter can lead to severe degradation of the result. In this paper, we present a parameter-free Plug-and-Play ADMMwhere internal parameters are updated as part of the optimization. Our algorithm is derived from the generalized approximate message passing, with several essential modifications. Experimentally, we find that the new algorithm produces solutions along a reliable and fast converging path.