From the Gradient-Step Denoiser to the Proximal Denoiser and their associated convergent Plug-and-Play algorithms

Vincent Herfeld, Baudouin Denis de Senneville, Arthur Leclaire, Nicolas Papadakis
9/11/2025
cs.LG

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Abstract

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.

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Cite this paper

@article{herfeld2025from,
  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},
  year   = {2025},
  eprint = {2509.09793},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2509.09793v1}
}

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