Uncovering the limits of uniqueness in sampled Gabor phase retrieval: A dense set of counterexamples in L2(ℝ)

Rima Alaifari, Francesca Bartolucci, Matthias Wellershoff

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

Abstract

Sampled Gabor phase retrieval — the problem of recovering a square-integrable signal from the magnitude of its Gabor transform sampled on a lattice — is a fundamental problem in signal processing, with important applications in areas such as imaging and audio processing. Recently, a classification of square-integrable signals which are not phase retrievable from Gabor measurements on parallel lines has been presented. This classification was used to exhibit a family of counterexamples to uniqueness in sampled Gabor phase retrieval. Here, we show that the set of counterexamples to uniqueness in sampled Gabor phase retrieval is dense in L2(ℝ), but is not equal to the whole of L2(ℝ) in general. Overall, our work contributes to a better understanding of the fundamental limits of sampled Gabor phase retrieval.
Original languageEnglish
Title of host publicationProceedings of the 2023 International Conference on Sampling Theory and Applications (SampTA)
PublisherIEEE
Number of pages5
ISBN (Electronic)979-8-3503-2885-1
ISBN (Print)979-8-3503-2886-8
DOIs
Publication statusPublished - 2023
Event 2023 International Conference on Sampling Theory and Applications (SampTA) - New Haven, United States
Duration: 10 Jul 202314 Jul 2023

Conference

Conference 2023 International Conference on Sampling Theory and Applications (SampTA)
Country/TerritoryUnited States
CityNew Haven
Period10/07/2314/07/23

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

  • Phase retrieval
  • Gabor transform
  • sampling result

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