Asymptotic Linear Convergence of ADMM for Isotropic TV Norm Compressed Sensing

[2505.01240] Asymptotic Linear Convergence of ADMM for Isotropic TV Norm Compressed Sensing Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Optimization and Control arXiv:2505.01240 (math) [Submitted on 2 May 2025 ( v1 ), last revised 24 Aug 2026 (this version, v4)] Title: Asymptotic Linear Convergence of ADMM for Isotropic TV Norm Compressed Sensing Authors: Emmanuel Gil Torres , Matt Jacobs , Xiangxiong Zhang View a PDF of the paper titled Asymptotic Linear Convergence of ADMM for Isotropic TV Norm Compressed Sensing, by Emmanuel Gil Torres and 2 other authors View PDF HTML (experimental) Abstract: We prove an explicit local linear rate for ADMM solving the isotropic Total Variation (TV) norm compressed sensing problem in multiple dimensions, by analyzing the auxiliary variable in the equivalent Douglas-Rachford splitting on a dual problem. Numerical verification on large 3D problems and real MRI data will be shown. Though the proven rate is not sharp, it is close to the observed ones in numerical tests. The proven rate is not sharp, but it provides an explicit upper bound that appears close to the observed convergence rate in numerical experiments, although we do not claim this behavior holds in general. Comments: 32 pages, 6 figures Subjects: Optimization and Control (math.OC) ; Numerical Analysis (math.NA) MSC classes: 90C25 (Primary) 65K05, 49J52 (Secondary) Cite as: arXiv:2505.01240 [math.OC] (or arXiv:2505.01240v4 [math.OC] for this version) https://doi.org/10.48550/arXiv.2505.01240 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Xiangxiong Zhang [ view email ] [v1] Fri, 2 May 2025 13:05:27 UTC (5,738 KB) [v2] Fri, 21 Nov 2025 00:47:04 UTC (5,678 KB) [v3] Wed, 8 Apr 2026 22:50:54 UTC (5,679 KB) [v4] Mon, 24 Aug 2026 01:42:54 UTC (5,669 KB) Full-text links: Access Paper: View a PDF of the paper titled Asymptotic Linear Convergence of ADMM for Isotropic TV Norm Compressed Sensing, by Emmanuel Gil Torres and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2025-05 Change to browse by: cs cs.NA math math.NA References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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