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dc.contributor.author
Kousholt, Astrid
dc.contributor.author
Schulte, Julia
dc.date.accessioned
2021-01-08T14:30:20Z
dc.date.available
2020-08-05T02:42:51Z
dc.date.available
2020-09-01T11:11:01Z
dc.date.available
2021-01-08T14:30:20Z
dc.date.issued
2021-01
dc.identifier.issn
0179-5376
dc.identifier.issn
1432-0444
dc.identifier.other
10.1007/s00454-020-00225-9
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/429982
dc.description.abstract
We investigate how much information about a convex body can be retrieved from a finite number of its geometric moments. We give a sufficient condition for a convex body to be uniquely determined by a finite number of its geometric moments, and we show that among all convex bodies, those which are uniquely determined by a finite number of moments form a dense set. Further, we derive a stability result for convex bodies based on geometric moments. It turns out that the stability result is improved considerably by using another set of moments, namely Legendre moments. We present a reconstruction algorithm that approximates a convex body using a finite number of its Legendre moments. The consistency of the algorithm is established using the stability result for Legendre moments. When only noisy measurements of Legendre moments are available, the consistency of the algorithm is established under certain assumptions on the variance of the noise variables. © 2020 Springer Nature Switzerland AG
en_US
dc.language.iso
en
en_US
dc.publisher
Springer
en_US
dc.subject
Convex body
en_US
dc.subject
Geometric moment
en_US
dc.subject
Legendre moment
en_US
dc.subject
Reconstruction
en_US
dc.subject
Uniqueness
en_US
dc.subject
Stability
en_US
dc.title
Reconstruction of Convex Bodies from Moments
en_US
dc.type
Journal Article
dc.date.published
2020-07-22
ethz.journal.title
Discrete & Computational Geometry
ethz.journal.volume
65
en_US
ethz.journal.issue
1
en_US
ethz.journal.abbreviated
Discrete comput. geom.
ethz.pages.start
1
en_US
ethz.pages.end
42
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Berlin
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02150 - Dep. Informatik / Dep. of Computer Science::02661 - Institut für Maschinelles Lernen / Institute for Machine Learning::09652 - Yang, Fan / Yang, Fan
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02150 - Dep. Informatik / Dep. of Computer Science::02661 - Institut für Maschinelles Lernen / Institute for Machine Learning::09652 - Yang, Fan / Yang, Fan
en_US
ethz.date.deposited
2020-08-05T02:42:56Z
ethz.source
WOS
ethz.eth
yes
en_US
ethz.availability
Metadata only
en_US
ethz.rosetta.installDate
2021-01-08T14:30:33Z
ethz.rosetta.lastUpdated
2021-02-15T23:02:06Z
ethz.rosetta.versionExported
true
ethz.COinS
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