Preconditioned Plug-and-Play ADMM with Locally Adjustable Denoiser for Image Restoration

TL;DR

This paper introduces a preconditioned plug-and-play ADMM framework with a locally adjustable denoiser, enabling improved image restoration by allowing pixel-wise noise control and enhancing various inverse imaging tasks.

Contribution

It extends plug-and-play ADMM to incorporate denoisers with spatially variable noise levels, supported by a new training procedure for pixel-wise adjustable CNN denoisers.

Findings

Enhanced image restoration performance in multiple tasks

Effective pixel-wise noise control improves results

Preconditioning justifies adjustable denoisers in ADMM

Abstract

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.