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dc.contributor.author
Alaifari, Rima
dc.contributor.author
Grohs, Philipp
dc.date.accessioned
2020-10-16T08:55:58Z
dc.date.available
2019-12-17T10:14:14Z
dc.date.available
2019-12-17T10:18:45Z
dc.date.available
2020-10-16T08:55:58Z
dc.date.issued
2021-01
dc.identifier.issn
1063-5203
dc.identifier.other
10.1016/j.acha.2019.09.003
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/386042
dc.description.abstract
The problem of reconstructing a function from the magnitudes of its frame coefficients has recently been shown to be never uniformly stable in infinite-dimensional spaces [5]. This result also holds for frames that are possibly continuous [2]. On the other hand, in finite-dimensional settings, unique solvability of the problem implies uniform stability. A prominent example of such a phase retrieval problem is the recovery of a signal from the modulus of its Gabor transform. In this paper, we study Gabor phase retrieval and ask how the stability degrades on a natural family of finite-dimensional subspaces of the signal domain L2 (R). We prove that the stability constant scales at least quadratically exponentially in the dimension of the subspaces. Our construction also shows that typical priors such as sparsity or smoothness promoting penalties do not constitute regularization terms for phase retrieval.
en_US
dc.language.iso
en
en_US
dc.publisher
Elsevier
en_US
dc.subject
Phase retrieval
en_US
dc.subject
Gabor transform
en_US
dc.subject
Stability
en_US
dc.title
Gabor phase retrieval is severely ill-posed
en_US
dc.type
Journal Article
dc.date.published
2019-09-22
ethz.journal.title
Applied and Computational Harmonic Analysis
ethz.journal.volume
50
en_US
ethz.journal.abbreviated
Appl. comput. harmon. anal. (Print)
ethz.pages.start
401
en_US
ethz.pages.end
419
en_US
ethz.identifier.scopus
ethz.publication.place
Amsterdam
en_US
ethz.publication.status
published
en_US
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
en_US
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
en_US
ethz.relation.isNewVersionOf
20.500.11850/297919
ethz.date.deposited
2019-12-17T10:14:25Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.availability
Metadata only
en_US
ethz.rosetta.installDate
2020-10-16T08:59:54Z
ethz.rosetta.lastUpdated
2020-10-16T08:59:54Z
ethz.rosetta.versionExported
true
ethz.COinS
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