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UNIQUENESS OF PHASE RETRIEVAL FROM THREE MEASUREMENTS

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorJAMING, Philippe
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorRATHMAIR, Martin
dc.date.accessioned2024-04-04T02:41:25Z
dc.date.available2024-04-04T02:41:25Z
dc.date.issued2023-08
dc.identifier.issn1019-7168
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191149
dc.description.abstractEnIn this paper we consider the question of finding an as small as possible family of operators $(T_j)_{j\in J}$ on $L^2(R)$ that does phase retrieval: every $\varphi$ is uniquely determined (up to a constant phase factor) by the phaseless data $(|T_j\varphi|)_{j\in J}$. This problem arises in various fields of applied sciences where usually the operators obey further restrictions. Of particular interest here are so-called {\em coded diffraction paterns} where the operators are of the form $T_j\varphi=\mathcal{F}m_j\varphi$, $\mathcal{F}$ the Fourier transform and $m_j\in L^\infty(R)$ are ``masks''. Here we explicitely construct three real-valued masks $m_1,m_2,m_3\in L^\infty(R)$ so that the associated coded diffraction patterns do phase retrieval. This implies that the three self-adjoint operators $T_j\varphi=\mathcal{F}[m_j\mathcal{F}^{-1}\varphi]$ also do phase retrieval. The proof uses complex analysis.We then show that some natural analogues of these operators in the finite dimensional setting do not always lead to the same uniqueness result due to an undersampling effect.
dc.language.isoen
dc.publisherSpringer Verlag
dc.title.enUNIQUENESS OF PHASE RETRIEVAL FROM THREE MEASUREMENTS
dc.typeArticle de revue
dc.identifier.doi10.1007/s10444-023-10045-z
dc.subject.halMathématiques [math]/Analyse classique [math.CA]
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.subject.halMathématiques [math]/Variables complexes [math.CV]
dc.identifier.arxiv2205.08753
bordeaux.journalAdvances in Computational Mathematics
bordeaux.page47
bordeaux.volume49
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue4
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03669715
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03669715v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Advances%20in%20Computational%20Mathematics&rft.date=2023-08&rft.volume=49&rft.issue=4&rft.spage=47&rft.epage=47&rft.eissn=1019-7168&rft.issn=1019-7168&rft.au=JAMING,%20Philippe&RATHMAIR,%20Martin&rft.genre=article


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