{"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/hppp-halpern-type-preconditioned-proximal","title":"HPPP: Halpern-type Preconditioned Proximal Point Algorithms and Applications to Image Restoration","arxiv_id":"2407.13120","date":"2024-07-18","proceeding":null,"authors":["Shuchang Zhang","HUI ZHANG","Hongxia Wang"],"abstract":"Recently, the degenerate preconditioned proximal point (PPP) method provides a unified and flexible framework for designing and analyzing operator-splitting algorithms such as Douglas-Rachford (DR). However, the degenerate PPP method exhibits weak convergence in the infinite-dimensional Hilbert space and lacks accelerated variants. To address these issues, we propose a Halpern-type PPP (HPPP) algorithm, which leverages the strong convergence and acceleration properties of Halpern's iteration method. Moreover, we propose a novel algorithm for image restoration by combining HPPP with denoiser priors such as Plug-and-Play (PnP) prior, which can be viewed as an accelerated PnP method. Finally, numerical experiments including several toy examples and image restoration validate the effectiveness of our proposed algorithms.","url_abs":"https://arxiv.org/abs/2407.13120v4","url_pdf":"https://arxiv.org/pdf/2407.13120v4.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":"hppp-halpern-type-preconditioned-proximal","repo_url":"https://github.com/zsc15/HPPP","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"deblurring","task_name":"Deblurring"},{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"image-deblurring","task_name":"Image Deblurring"},{"task_slug":"image-restoration","task_name":"Image Restoration"}],"methods":[{"method_slug":"pixel-prediction","method_name":"Inpainting"},{"method_slug":"pnp","method_name":"PnP"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}