{"ID":2872332,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.09793","arxiv_id":"2509.09793","title":"From the Gradient-Step Denoiser to the Proximal Denoiser and their associated convergent Plug-and-Play algorithms","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.","short_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...","url_abs":"https://arxiv.org/abs/2509.09793","url_pdf":"https://arxiv.org/pdf/2509.09793v1","authors":"[\"Vincent Herfeld\",\"Baudouin Denis de Senneville\",\"Arthur Leclaire\",\"Nicolas Papadakis\"]","published":"2025-09-11T18:53:08Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}