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dc.contributor.author
Alaifari, Rima
dc.contributor.author
Wellershoff, Matthias
dc.date.accessioned
2021-03-16T12:23:31Z
dc.date.available
2021-03-14T05:25:17Z
dc.date.available
2021-03-16T12:23:31Z
dc.date.issued
2021
dc.identifier.issn
1069-5869
dc.identifier.issn
1531-5851
dc.identifier.other
10.1007/s00041-020-09802-1
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/474334
dc.identifier.doi
10.3929/ethz-b-000474334
dc.description.abstract
Phase retrieval refers to the problem of recovering some signal (which is often modelled as an element of a Hilbert space) from phaseless measurements. It has been shown that in the deterministic setting phase retrieval from frame coefficients is always unstable in infinite-dimensional Hilbert spaces (Cahill et al. in Trans Am Math Soc Ser B 3(3):63–76, 2016) and possibly severely ill-conditioned in finite-dimensional Hilbert spaces (Cahill et al. in Trans Am Math Soc Ser B 3(3):63–76, 2016). Recently, it has also been shown that phase retrieval from measurements induced by the Gabor transform with Gaussian window function is stable under a more relaxed semi-global phase recovery regime based on atoll functions (Alaifari in Found Comput Math 19(4):869–900, 2019). In finite dimensions, we present first evidence that this semi-global reconstruction regime allows one to do phase retrieval from measurements of bandlimited signals induced by the discrete Gabor transform in such a way that the corresponding stability constant only scales like a low order polynomial in the space dimension. To this end, we utilise reconstruction formulae which have become common tools in recent years (Bojarovska and Flinth in J Fourier Anal Appl 22(3):542–567, 2016; Eldar et al. in IEEE Signal Process Lett 22(5):638–642, 2014; Li et al. in IEEE Signal Process Lett 24(4):372–376, 2017; Nawab et al. in IEEE Trans Acoust Speech Signal Process 31(4):986–998, 1983).
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dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Birkhäuser
en_US
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
dc.subject
Phase retrieval
en_US
dc.subject
Gabor frames
en_US
dc.subject
Time-frequency analysis
en_US
dc.title
Stability Estimates for Phase Retrieval from Discrete Gabor Measurements
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution 4.0 International
dc.date.published
2021-02-19
ethz.journal.title
Journal of Fourier Analysis and Applications
ethz.journal.volume
27
en_US
ethz.journal.issue
2
en_US
ethz.journal.abbreviated
J Fourier Anal Appl
ethz.pages.start
6
en_US
ethz.size
31 p.
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ethz.version.deposit
publishedVersion
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ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Basel
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ethz.publication.status
published
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ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::09603 - Alaifari, Rima / Alaifari, Rima
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::09603 - Alaifari, Rima / Alaifari, Rima
ethz.relation.isCitedBy
10.3929/ethz-b-000548828
ethz.date.deposited
2021-03-14T05:25:28Z
ethz.source
SCOPUS
ethz.eth
yes
en_US
ethz.availability
Open access
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ethz.rosetta.installDate
2021-03-16T12:23:42Z
ethz.rosetta.lastUpdated
2022-03-29T05:48:37Z
ethz.rosetta.versionExported
true
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