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 language | English |
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Title of host publication | Proceedings of the 2023 International Conference on Sampling Theory and Applications (SampTA) |
Publisher | IEEE |
Number of pages | 5 |
ISBN (Electronic) | 979-8-3503-2885-1 |
ISBN (Print) | 979-8-3503-2886-8 |
DOIs | |
Publication status | Published - 2023 |
Event | 2023 International Conference on Sampling Theory and Applications (SampTA) - New Haven, United States Duration: 10 Jul 2023 → 14 Jul 2023 |
Conference
Conference | 2023 International Conference on Sampling Theory and Applications (SampTA) |
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Country/Territory | United States |
City | New Haven |
Period | 10/07/23 → 14/07/23 |
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-careOtherwise 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