{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/proximal-denoiser-for-convergent-plug-and","title":"Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularization","arxiv_id":"2201.13256","date":"2022-01-31","proceeding":null,"authors":["Samuel Hurault","Arthur Leclaire","Nicolas Papadakis"],"abstract":"Plug-and-Play (PnP) methods solve ill-posed inverse problems through iterative proximal algorithms by replacing a proximal operator by a denoising operation. When applied with deep neural network denoisers, these methods have shown state-of-the-art visual performance for image restoration problems. However, their theoretical convergence analysis is still incomplete. Most of the existing convergence results consider nonexpansive denoisers, which is non-realistic, or limit their analysis to strongly convex data-fidelity terms in the inverse problem to solve. Recently, it was proposed to train the denoiser as a gradient descent step on a functional parameterized by a deep neural network. Using such a denoiser guarantees the convergence of the PnP version of the Half-Quadratic-Splitting (PnP-HQS) iterative algorithm. In this paper, we show that this gradient denoiser can actually correspond to the proximal operator of another scalar function. Given this new result, we exploit the convergence theory of proximal algorithms in the nonconvex setting to obtain convergence results for PnP-PGD (Proximal Gradient Descent) and PnP-ADMM (Alternating Direction Method of Multipliers). When built on top of a smooth gradient denoiser, we show that PnP-PGD and PnP-ADMM are convergent and target stationary points of an explicit functional. These convergence results are confirmed with numerical experiments on deblurring, super-resolution and inpainting.","url_abs":"https://arxiv.org/abs/2201.13256v4","url_pdf":"https://arxiv.org/pdf/2201.13256v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"proximal-denoiser-for-convergent-plug-and","repo_url":"https://github.com/samuro95/prox-pnp","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"deblurring","task_name":"Deblurring"},{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"image-restoration","task_name":"Image Restoration"},{"task_slug":"super-resolution","task_name":"Super-Resolution"}],"methods":[{"method_slug":"pnp","method_name":"PnP"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2201.13256","atlas_url":"https://app.syntology.ai/?focus=2201.13256","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2201.13256"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/samuro95/prox-pnp","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"ran":6,"unverified":3},"by_repo_kind":{"official":{"samples":9,"ran":6,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"a5f896944a03d905","entry":"blockproc","repo":"samuro95/prox-pnp","repo_kind":"official","path":"PnP_restoration/utils/utils_sr.py","file_url":"https://github.com/samuro95/prox-pnp/blob/HEAD/PnP_restoration/utils/utils_sr.py","link_basis":"harvester_set","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"a5f896944a03d905"}},{"code_sha256_prefix":"a94cdf48560711e9","entry":"fun_reshape","repo":"samuro95/prox-pnp","repo_kind":"official","path":"PnP_restoration/utils/utils_sr.py","file_url":"https://github.com/samuro95/prox-pnp/blob/HEAD/PnP_restoration/utils/utils_sr.py","link_basis":"harvester_set","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"a94cdf48560711e9"}},{"code_sha256_prefix":"9fe27315fe97ae9b","entry":"get_rho_sigma","repo":"samuro95/prox-pnp","repo_kind":"official","path":"PnP_restoration/utils/utils_deblur.py","file_url":"https://github.com/samuro95/prox-pnp/blob/HEAD/PnP_restoration/utils/utils_deblur.py","link_basis":"harvester_set","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"9fe27315fe97ae9b"}},{"code_sha256_prefix":"8c6468052b1b52eb","entry":"modcrop","repo":"samuro95/prox-pnp","repo_kind":"official","path":"PnP_restoration/utils/utils_restoration.py","file_url":"https://github.com/samuro95/prox-pnp/blob/HEAD/PnP_restoration/utils/utils_restoration.py","link_basis":"harvester_set","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"8c6468052b1b52eb"}},{"code_sha256_prefix":"5cb805290cf1d779","entry":"otf2psf","repo":"samuro95/prox-pnp","repo_kind":"official","path":"PnP_restoration/utils/utils_deblur.py","file_url":"https://github.com/samuro95/prox-pnp/blob/HEAD/PnP_restoration/utils/utils_deblur.py","link_basis":"harvester_set","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"5cb805290cf1d779"}},{"code_sha256_prefix":"a05624ca6ad6870e","entry":"randomCrop","repo":"samuro95/prox-pnp","repo_kind":"official","path":"PnP_restoration/utils/utils_restoration.py","file_url":"https://github.com/samuro95/prox-pnp/blob/HEAD/PnP_restoration/utils/utils_restoration.py","link_basis":"harvester_set","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"a05624ca6ad6870e"}},{"code_sha256_prefix":"fb5d5779350ffe96","entry":"fun_mul","repo":"samuro95/prox-pnp","repo_kind":"official","path":"PnP_restoration/utils/utils_sr.py","file_url":"https://github.com/samuro95/prox-pnp/blob/HEAD/PnP_restoration/utils/utils_sr.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"fb5d5779350ffe96"}},{"code_sha256_prefix":"df2f94719784027b","entry":"get_uperleft_denominator","repo":"samuro95/prox-pnp","repo_kind":"official","path":"PnP_restoration/utils/utils_deblur.py","file_url":"https://github.com/samuro95/prox-pnp/blob/HEAD/PnP_restoration/utils/utils_deblur.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"df2f94719784027b"}},{"code_sha256_prefix":"72d98b47ea73bd56","entry":"imread_uint","repo":"samuro95/prox-pnp","repo_kind":"official","path":"PnP_restoration/utils/utils_restoration.py","file_url":"https://github.com/samuro95/prox-pnp/blob/HEAD/PnP_restoration/utils/utils_restoration.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"72d98b47ea73bd56"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}