Phase retrieval of bandlimited functions for the wavelet transform

[2009.05029] Phase retrieval of bandlimited functions for the wavelet transform Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Functional Analysis arXiv:2009.05029 (math) [Submitted on 10 Sep 2020 ( v1 ), last revised 5 Nov 2021 (this version, v5)] Title: Phase retrieval of bandlimited functions for the wavelet transform Authors: Rima Alaifari , Francesca Bartolucci , Matthias Wellershoff View a PDF of the paper titled Phase retrieval of bandlimited functions for the wavelet transform, by Rima Alaifari and 1 other authors View PDF HTML (experimental) Abstract: We study the recovery of square-integrable signals from the absolute values of their wavelet transforms, also called wavelet phase retrieval. We present a new uniqueness result for wavelet phase retrieval. To be precise, we show that any wavelet with finitely many vanishing moments allows for the unique recovery of real-valued bandlimited signals up to global sign. Additionally, we present the first uniqueness result for sampled wavelet phase retrieval in which the underlying wavelets are allowed to be complex-valued and we present a uniqueness result for phase retrieval from sampled Cauchy wavelet transform measurements. Comments: 18 pages Subjects: Functional Analysis (math.FA) Cite as: arXiv:2009.05029 [math.FA] (or arXiv:2009.05029v5 [math.FA] for this version) https://doi.org/10.48550/arXiv.2009.05029 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Applied and Computational Harmonic Analysis 64 (2023) 102-117 Related DOI : https://doi.org/10.1016/j.acha.2023.01.002 Focus to learn more DOI(s) linking to related resources Submission history From: Francesca Bartolucci [ view email ] [v1] Thu, 10 Sep 2020 17:50:43 UTC (25 KB) [v2] Fri, 11 Sep 2020 14:04:05 UTC (14 KB) [v3] Wed, 21 Oct 2020 07:54:42 UTC (27 KB) [v4] Thu, 22 Oct 2020 16:27:37 UTC (27 KB) [v5] Fri, 5 Nov 2021 14:25:41 UTC (23 KB) Full-text links: Access Paper: View a PDF of the paper titled Phase retrieval of bandlimited functions for the wavelet transform, by Rima Alaifari and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.FA < prev | next > new | recent | 2020-09 Change to browse by: math 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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