In this paper we analyze the Gradient-Step Denoiser and its usage in Plug-and-Play algorithms. The Plug-and-Play paradigm of optimization algorithms uses off the shelf denoisers to replace a proximity operator or a gradient descent operator of an image prior. Usually this image prior is implicit and cannot be expressed, but the Gradient-Step Denoiser is trained to be exactly the gradient descent operator or the proximity operator of an explicit functional while preserving state-of-the-art denoising capabilities.
@article{arxiv.2509.09793,
title = {From the Gradient-Step Denoiser to the Proximal Denoiser and their associated convergent Plug-and-Play algorithms},
author = {Vincent Herfeld and Baudouin Denis de Senneville and Arthur Leclaire and Nicolas Papadakis},
journal= {arXiv preprint arXiv:2509.09793},
year = {2025}
}