{"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/plug-in-estimation-in-high-dimensional-linear-1","title":"Plug-in Estimation in High-Dimensional Linear Inverse Problems: A Rigorous Analysis","arxiv_id":"1806.10466","date":"2018-06-27","proceeding":null,"authors":["Alyson K. Fletcher","Sundeep Rangan","Subrata Sarkar","Philip Schniter"],"abstract":"Estimating a vector $\\mathbf{x}$ from noisy linear measurements $\\mathbf{Ax}+\\mathbf{w}$ often requires use of prior knowledge or structural constraints on $\\mathbf{x}$ for accurate reconstruction. Several recent works have considered combining linear least-squares estimation with a generic or \"plug-in\" denoiser function that can be designed in a modular manner based on the prior knowledge about $\\mathbf{x}$. While these methods have shown excellent performance, it has been difficult to obtain rigorous performance guarantees. This work considers plug-in denoising combined with the recently-developed Vector Approximate Message Passing (VAMP) algorithm, which is itself derived via Expectation Propagation techniques. It shown that the mean squared error of this \"plug-and-play\" VAMP can be exactly predicted for high-dimensional right-rotationally invariant random $\\mathbf{A}$ and Lipschitz denoisers. The method is demonstrated on applications in image recovery and parametric bilinear estimation.","url_abs":"https://arxiv.org/abs/1806.10466v3","url_pdf":"https://arxiv.org/pdf/1806.10466v3.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"plug-in-estimation-in-high-dimensional-linear-1","repo_url":"https://github.com/ricedsp/D-AMP_Toolbox","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1806.10466","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}