Applied Inverse Problems Conference (2023)

Abstract

Plug-and-Play (PnP) methods constitute a class of iterative algorithms for imaging problems where regularization is performed by an off-the-shelf denoiser. Specifically, given an image dataset, optimizing a function (e.g. a neural network) to remove Gaussian noise is equivalent to approximating the gradient or the proximal operator of the log prior of the training dataset. Therefore, any off-the-shelf denoiser can be used as an implicit prior and inserted into an optimization scheme to restore images. The PnP and Regularization by Denoising (RED) frameworks provide a basis for this approach, for which various convergence analyses have been proposed in the literature. However, most existing results require either unverifiable or suboptimal hypotheses on the denoiser, or assume restrictive conditions on the parameters of the inverse problem. We will introduce the Gradient Step and Proximal denoisers, and their variants, recently proposed to restore RED and PnP algorithms to their original form as (nonconvex) real proximal splitting algorithms. These new algorithms are shown to converge towards stationary points of an explicit functional and to perform state-of-the-art image restoration, both quantitatively and qualitatively.

Samuel Hurault

Mathematics, Machine Learning, Computer Vision