X-ray tomography of one-forms with partial data

Joonas Ilmavirta; Keijo Mönkkönen

doi:10.1137/20M1344779

X-ray tomography of one-forms with partial data

Joonas Ilmavirta
, Keijo Mönkkönen

Tietotekniikka

Tutkimustuotos: Artikkeli › Tieteellinen › vertaisarvioitu

7 Sitaatiot (Scopus)

Abstrakti

If the integrals of a one-form over all lines meeting a small open set vanish and the form is closed in this set, then the one-form is exact in the whole Euclidean space. We obtain a unique continuation result for the normal operator of the x-ray transform of one-forms, and this leads to one of our two proofs of the partial data result. Our proofs apply to compactly supported covector-valued distributions.

Alkuperäiskieli	Englanti
Sivut	3002–3015
Sivumäärä	14
Julkaisu	SIAM Journal on Mathematical Analysis
Vuosikerta	53
Numero	3
DOI - pysyväislinkit	https://doi.org/10.1137/20M1344779
Tila	Julkaistu - 20 toukok. 2021
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Rahoitus

\ast Received by the editors June 11, 2020; accepted for publication (in revised form) March 3, 2021; published electronically May 20, 2021. https://doi.org/10.1137/20M1344779 Funding: The work of the first author was supported by the Academy of Finland grants 332890, 336254. The work of the second author was supported by the Academy of Finland (Centre of Excellence in Inverse Modelling and Imaging) grants 284715, 309963. \dagger Unit of Computing Sciences, Tampere University, Kalevantie 4, FI-33014 Tampere University, Finland ([email protected]). \ddagger Department of Mathematics and Statistics, University of Jyv\a"skyl\a", P.O. Box 35 (MaD) FI-40014 University of Jyv\a"skyl\a", Finland ([email protected]).

Julkaisufoorumi-taso

Jufo-taso 2

!!ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

Pääsy asiakirjaan

10.1137/20M1344779

http://urn.fi/URN:NBN:fi:jyu-202107144312

Siteeraa tätä

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abstract = "If the integrals of a one-form over all lines meeting a small open set vanish and the form is closed in this set, then the one-form is exact in the whole Euclidean space. We obtain a unique continuation result for the normal operator of the x-ray transform of one-forms, and this leads to one of our two proofs of the partial data result. Our proofs apply to compactly supported covector-valued distributions.",

keywords = "Inverse problems, Normal operator, Unique continuation, Vector field tomography, X-ray tomography",

author = "Joonas Ilmavirta and Keijo M{\"o}nkk{\"o}nen",

note = "Funding Information: \textbackslash{}ast Received by the editors June 11, 2020; accepted for publication (in revised form) March 3, 2021; published electronically May 20, 2021. https://doi.org/10.1137/20M1344779 Funding: The work of the first author was supported by the Academy of Finland grants 332890, 336254. The work of the second author was supported by the Academy of Finland (Centre of Excellence in Inverse Modelling and Imaging) grants 284715, 309963. \textbackslash{}dagger Unit of Computing Sciences, Tampere University, Kalevantie 4, FI-33014 Tampere University, Finland ([email protected]). \textbackslash{}ddagger Department of Mathematics and Statistics, University of Jyv\textbackslash{}a{"}skyl\textbackslash{}a{"}, P.O. Box 35 (MaD) FI-40014 University of Jyv\textbackslash{}a{"}skyl\textbackslash{}a{"}, Finland ([email protected]). Publisher Copyright: {\textcopyright} 2021 Society for Industrial and Applied Mathematics",

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AU - Ilmavirta, Joonas

AU - Mönkkönen, Keijo

N1 - Funding Information: \ast Received by the editors June 11, 2020; accepted for publication (in revised form) March 3, 2021; published electronically May 20, 2021. https://doi.org/10.1137/20M1344779 Funding: The work of the first author was supported by the Academy of Finland grants 332890, 336254. The work of the second author was supported by the Academy of Finland (Centre of Excellence in Inverse Modelling and Imaging) grants 284715, 309963. \dagger Unit of Computing Sciences, Tampere University, Kalevantie 4, FI-33014 Tampere University, Finland ([email protected]). \ddagger Department of Mathematics and Statistics, University of Jyv\a"skyl\a", P.O. Box 35 (MaD) FI-40014 University of Jyv\a"skyl\a", Finland ([email protected]). Publisher Copyright: © 2021 Society for Industrial and Applied Mathematics

PY - 2021/5/20

Y1 - 2021/5/20

N2 - If the integrals of a one-form over all lines meeting a small open set vanish and the form is closed in this set, then the one-form is exact in the whole Euclidean space. We obtain a unique continuation result for the normal operator of the x-ray transform of one-forms, and this leads to one of our two proofs of the partial data result. Our proofs apply to compactly supported covector-valued distributions.

AB - If the integrals of a one-form over all lines meeting a small open set vanish and the form is closed in this set, then the one-form is exact in the whole Euclidean space. We obtain a unique continuation result for the normal operator of the x-ray transform of one-forms, and this leads to one of our two proofs of the partial data result. Our proofs apply to compactly supported covector-valued distributions.

KW - Inverse problems

KW - Normal operator

KW - Unique continuation

KW - Vector field tomography

KW - X-ray tomography

U2 - 10.1137/20M1344779

DO - 10.1137/20M1344779

M3 - Article

AN - SCOPUS:85107516630

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SP - 3002

EP - 3015

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 3

ER -

X-ray tomography of one-forms with partial data

Abstrakti

Rahoitus

Julkaisufoorumi-taso

!!ASJC Scopus subject areas

Pääsy asiakirjaan

Sormenjälki

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