The generic crystallographic phase retrieval problem

[2307.06835] The generic crystallographic phase retrieval problem Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Functional Analysis arXiv:2307.06835 (math) [Submitted on 13 Jul 2023 ( v1 ), last revised 30 Apr 2026 (this version, v3)] Title: The generic crystallographic phase retrieval problem Authors: Dan Edidin , Arun Suresh View a PDF of the paper titled The generic crystallographic phase retrieval problem, by Dan Edidin and 1 other authors View PDF HTML (experimental) Abstract: In this paper we consider the problem of recovering a signal $x \in \mathbb{R}^N$ from its power spectrum assuming that the signal is sparse with respect to a generic basis for $\mathbb{R}^N$. Our main result is that if the sparsity level is at most $\sim\! N/2$ in this basis then the generic sparse vector is uniquely determined up to sign from its power spectrum. We also prove that if the sparsity level is $\sim\! N/4$ then every sparse vector is determined up to sign from its power spectrum. Analogous results are also obtained for the power spectrum of a vector in $\mathbb{C}^N$ which extend earlier results of Wang and Xu \cite{ arXiv:1310.0873 }. Comments: 20 pages Subjects: Functional Analysis (math.FA) ; Information Theory (cs.IT); Algebraic Geometry (math.AG) MSC classes: 42A10, 94A12, 94A15 Cite as: arXiv:2307.06835 [math.FA] (or arXiv:2307.06835v3 [math.FA] for this version) https://doi.org/10.48550/arXiv.2307.06835 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Dan Edidin [ view email ] [v1] Thu, 13 Jul 2023 15:56:14 UTC (23 KB) [v2] Mon, 24 Jul 2023 20:05:40 UTC (23 KB) [v3] Thu, 30 Apr 2026 22:07:23 UTC (24 KB) Full-text links: Access Paper: View a PDF of the paper titled The generic crystallographic phase retrieval problem, by Dan Edidin and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.FA < prev | next > new | recent | 2023-07 Change to browse by: cs cs.IT math math.AG math.IT 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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