  Plug-and-Play optimization recently emerged as a powerful technique for
solving inverse problems by plugging a denoiser into a classical optimization
algorithm. The denoiser accounts for the regularization and therefore
implicitly determines the prior knowledge on the data, hence replacing typical
handcrafted priors. In this paper, we extend the concept of plug-and-play
optimization to use denoisers that can be parameterized for non-constant noise
variance. In that aim, we introduce a preconditioning of the ADMM algorithm,
which mathematically justifies the use of such an adjustable denoiser. We
additionally propose a procedure for training a convolutional neural network
for high quality non-blind image denoising that also allows for pixel-wise
control of the noise standard deviation. We show that our pixel-wise adjustable
denoiser, along with a suitable preconditioning strategy, can further improve
the plug-and-play ADMM approach for several applications, including image
completion, interpolation, demosaicing and Poisson denoising.
