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The Nyquist sampling rate for spiraling curves

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorJAMING, Philippe
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorNEGREIRA, Felipe
hal.structure.identifierFakultät für Mathematik [Wien]
hal.structure.identifierAcoustics Research Institute [ARI]
dc.contributor.authorROMERO, José Luis
dc.date.accessioned2024-04-04T03:00:51Z
dc.date.available2024-04-04T03:00:51Z
dc.date.issued2021
dc.identifier.issn1063-5203
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192849
dc.description.abstractEnWe consider the problem of reconstructing a compactly supported function from samples of its Fourier transform taken along a spiral. We determine the Nyquist sampling rate in terms of the density of the spiral and show that below this rate spirals suffer from an approximate form of aliasing. This sets a limit to the amount of undersampling that compressible signals admit when sampled along spirals. More precisely, we derive a lower bound on the condition number for the reconstruction of functions of bounded variation, and for functions that are sparse in the Haar wavelet basis.
dc.language.isoen
dc.publisherElsevier
dc.title.enThe Nyquist sampling rate for spiraling curves
dc.typeArticle de revue
dc.identifier.doi10.1016/j.acha.2020.01.005
dc.subject.halMathématiques [math]/Analyse classique [math.CA]
dc.subject.halSciences de l'ingénieur [physics]/Traitement du signal et de l'image
dc.identifier.arxiv1811.01771
bordeaux.journalApplied and Computational Harmonic Analysis
bordeaux.page198-230
bordeaux.volume52
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01898240
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01898240v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Applied%20and%20Computational%20Harmonic%20Analysis&rft.date=2021&rft.volume=52&rft.spage=198-230&rft.epage=198-230&rft.eissn=1063-5203&rft.issn=1063-5203&rft.au=JAMING,%20Philippe&NEGREIRA,%20Felipe&ROMERO,%20Jos%C3%A9%20Luis&rft.genre=article


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