ON THE EFFECT OF ZERO-FLIPPING ON THE STABILITY OF THE PHASE RETRIEVAL PROBLEM IN THE PALEY-WIENER CLASS
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | JAMING, Philippe | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | KELLAY, Karim | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Institute of Mathematics, University of the Philippines Diliman | |
| dc.contributor.author | PEREZ, Rolando | |
| dc.date.accessioned | 2024-04-04T02:46:59Z | |
| dc.date.available | 2024-04-04T02:46:59Z | |
| dc.date.issued | 2022-08 | |
| dc.identifier.issn | 0026-9255 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191602 | |
| dc.description.abstractEn | In the classical phase retrieval problem in the Paley-Wiener class $PW_L$ for $L>0$, \textit{i.e.} to recover $f\in PW_L$ from $|f|$, Akutowicz, Walther, and Hofstetter independently showed that all such solutions can be obtained by flipping an arbitrary set of complex zeros across the real line. This operation is called zero-flipping and we denote by $\mathfrak{F}_a f$ the resulting function. The operator $\mathfrak{F}_a$ is defined even if $a$ is not a genuine zero of $f$, that is if we make an error on the location of the zero. Our main goal is to investigate the effect of $\mathfrak{F}_a$. We show that $\mathfrak{F}_af$ is no longer bandlimited but is still wide-banded. We then investigate the effect of $\mathfrak{F}_a$ on the stability of phase retrieval by estimating the quantity $\inf_{|c|=1}\|cf-\mathfrak{F}_af\|_2$. We show that this quantity is in general not well-suited to investigate stability, and so we introduce the quantity $\inf_{|c|=1}\|c\mathfrak{F}_bf-\mathfrak{F}_af\|_2$. We show that this quantity is dominated by the distance between $a$ and $b$. | |
| dc.description.sponsorship | Noyaux reproduisants en Analyse et au-delà - ANR-18-CE40-0035 | |
| dc.language.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.subject.en | phase retrieval | |
| dc.subject.en | Paley-Wiener class | |
| dc.subject.en | zero-flipping | |
| dc.subject.en | stability | |
| dc.title.en | ON THE EFFECT OF ZERO-FLIPPING ON THE STABILITY OF THE PHASE RETRIEVAL PROBLEM IN THE PALEY-WIENER CLASS | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s00605-022-01716-y | |
| dc.subject.hal | Mathématiques [math]/Analyse classique [math.CA] | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.subject.hal | Mathématiques [math]/Variables complexes [math.CV] | |
| dc.identifier.arxiv | 2103.05937 | |
| bordeaux.journal | Monatshefte für Mathematik | |
| bordeaux.page | 757-776 | |
| bordeaux.volume | 198 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 4 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-03164251 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03164251v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Monatshefte%20f%C3%BCr%20Mathematik&rft.date=2022-08&rft.volume=198&rft.issue=4&rft.spage=757-776&rft.epage=757-776&rft.eissn=0026-9255&rft.issn=0026-9255&rft.au=JAMING,%20Philippe&KELLAY,%20Karim&PEREZ,%20Rolando&rft.genre=article |
Files in this item
| Files | Size | Format | View |
|---|---|---|---|
|
There are no files associated with this item. |
|||