{"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/provably-convergent-plug-and-play-quasi","title":"Provably Convergent Plug-and-Play Quasi-Newton Methods","arxiv_id":"2303.07271","date":"2023-03-09","proceeding":null,"authors":["Hong Ye Tan","Subhadip Mukherjee","Junqi Tang","Carola-Bibiane Schönlieb"],"abstract":"Plug-and-Play (PnP) methods are a class of efficient iterative methods that aim to combine data fidelity terms and deep denoisers using classical optimization algorithms, such as ISTA or ADMM, with applications in inverse problems and imaging. Provable PnP methods are a subclass of PnP methods with convergence guarantees, such as fixed point convergence or convergence to critical points of some energy function. Many existing provable PnP methods impose heavy restrictions on the denoiser or fidelity function, such as non-expansiveness or strict convexity, respectively. In this work, we propose a novel algorithmic approach incorporating quasi-Newton steps into a provable PnP framework based on proximal denoisers, resulting in greatly accelerated convergence while retaining light assumptions on the denoiser. By characterizing the denoiser as the proximal operator of a weakly convex function, we show that the fixed points of the proposed quasi-Newton PnP algorithm are critical points of a weakly convex function. Numerical experiments on image deblurring and super-resolution demonstrate 2--8x faster convergence as compared to other provable PnP methods with similar reconstruction quality.","url_abs":"https://arxiv.org/abs/2303.07271v4","url_pdf":"https://arxiv.org/pdf/2303.07271v4.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":"provably-convergent-plug-and-play-quasi","repo_url":"https://github.com/hyt35/prox-qn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"deblurring","task_name":"Deblurring"},{"task_slug":"image-deblurring","task_name":"Image Deblurring"},{"task_slug":"super-resolution","task_name":"Super-Resolution"}],"methods":[{"method_slug":"admm","method_name":"ADMM"},{"method_slug":"pnp","method_name":"PnP"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2303.07271","atlas_url":"https://app.syntology.ai/?focus=2303.07271","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2303.07271"}},"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/hyt35/prox-qn","reach":null}],"summary":{"ran_violates":1},"by_repo_kind":{"official":{"samples":1,"ran":1,"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":"1ddc874088c80869","entry":"normalize_min_max","repo":"hyt35/prox-qn","repo_kind":"official","path":"GS_denoising/GS_utils.py","file_url":"https://github.com/hyt35/prox-qn/blob/HEAD/GS_denoising/GS_utils.py","link_basis":"first_harvest_node","language":"python","status":"ran_violates","verification_level":1,"contract_check":"VIOLATES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"1ddc874088c80869"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}