Matches in SemOpenAlex for { <https://semopenalex.org/work/W2080992495> ?p ?o ?g. }
Showing items 1 to 88 of
88
with 100 items per page.
- W2080992495 endingPage "4" @default.
- W2080992495 startingPage "1" @default.
- W2080992495 abstract "The cone beam transform of a tensor field of order<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=E2><mml:mi>m</mml:mi></mml:math>in<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=E3><mml:mrow><mml:mi>n</mml:mi><mml:mo>≥</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math>dimensions is considered. We prove that the image of a tensor field under this transform is related to a derivative of the<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=E4><mml:mi>n</mml:mi></mml:math>-dimensional Radon transform applied to a projection of the tensor field. Actually the relation we show reduces for<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=E5><mml:mrow><mml:mi>m</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=E6><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math>to the well-known formula of Grangeat. In that sense, the paper contains a generalization of Grangeat's formula to arbitrary tensor fields in any dimension. We further briefly explain the importance of that formula for the problem of tensor field tomography. Unfortunately, for<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=E7><mml:mrow><mml:mi>m</mml:mi><mml:mo>></mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>, an inversion method cannot be derived immediately. Thus, we point out the possibility to calculate reconstruction kernels for the cone beam transform using Grangeat's formula." @default.
- W2080992495 created "2016-06-24" @default.
- W2080992495 creator A5083589911 @default.
- W2080992495 date "2007-01-01" @default.
- W2080992495 modified "2023-10-17" @default.
- W2080992495 title "The Formula of Grangeat for Tensor Fields of Arbitrary Order innDimensions" @default.
- W2080992495 cites W1806897574 @default.
- W2080992495 cites W1977506423 @default.
- W2080992495 cites W2011016066 @default.
- W2080992495 cites W2023749508 @default.
- W2080992495 cites W2025650106 @default.
- W2080992495 cites W2028080603 @default.
- W2080992495 cites W2147585767 @default.
- W2080992495 cites W2169835892 @default.
- W2080992495 cites W2952379075 @default.
- W2080992495 cites W4238349935 @default.
- W2080992495 doi "https://doi.org/10.1155/2007/12839" @default.
- W2080992495 hasPubMedCentralId "https://www.ncbi.nlm.nih.gov/pmc/articles/1906704" @default.
- W2080992495 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/17713588" @default.
- W2080992495 hasPublicationYear "2007" @default.
- W2080992495 type Work @default.
- W2080992495 sameAs 2080992495 @default.
- W2080992495 citedByCount "2" @default.
- W2080992495 countsByYear W20809924952013 @default.
- W2080992495 crossrefType "journal-article" @default.
- W2080992495 hasAuthorship W2080992495A5083589911 @default.
- W2080992495 hasBestOaLocation W20809924951 @default.
- W2080992495 hasConcept C109007969 @default.
- W2080992495 hasConcept C11413529 @default.
- W2080992495 hasConcept C127313418 @default.
- W2080992495 hasConcept C134306372 @default.
- W2080992495 hasConcept C148125525 @default.
- W2080992495 hasConcept C151730666 @default.
- W2080992495 hasConcept C155281189 @default.
- W2080992495 hasConcept C166077713 @default.
- W2080992495 hasConcept C177148314 @default.
- W2080992495 hasConcept C1893757 @default.
- W2080992495 hasConcept C197231052 @default.
- W2080992495 hasConcept C20178491 @default.
- W2080992495 hasConcept C202444582 @default.
- W2080992495 hasConcept C33676613 @default.
- W2080992495 hasConcept C33923547 @default.
- W2080992495 hasConcept C520416788 @default.
- W2080992495 hasConcept C57493831 @default.
- W2080992495 hasConcept C9652623 @default.
- W2080992495 hasConceptScore W2080992495C109007969 @default.
- W2080992495 hasConceptScore W2080992495C11413529 @default.
- W2080992495 hasConceptScore W2080992495C127313418 @default.
- W2080992495 hasConceptScore W2080992495C134306372 @default.
- W2080992495 hasConceptScore W2080992495C148125525 @default.
- W2080992495 hasConceptScore W2080992495C151730666 @default.
- W2080992495 hasConceptScore W2080992495C155281189 @default.
- W2080992495 hasConceptScore W2080992495C166077713 @default.
- W2080992495 hasConceptScore W2080992495C177148314 @default.
- W2080992495 hasConceptScore W2080992495C1893757 @default.
- W2080992495 hasConceptScore W2080992495C197231052 @default.
- W2080992495 hasConceptScore W2080992495C20178491 @default.
- W2080992495 hasConceptScore W2080992495C202444582 @default.
- W2080992495 hasConceptScore W2080992495C33676613 @default.
- W2080992495 hasConceptScore W2080992495C33923547 @default.
- W2080992495 hasConceptScore W2080992495C520416788 @default.
- W2080992495 hasConceptScore W2080992495C57493831 @default.
- W2080992495 hasConceptScore W2080992495C9652623 @default.
- W2080992495 hasFunder F4320320879 @default.
- W2080992495 hasLocation W20809924951 @default.
- W2080992495 hasLocation W20809924952 @default.
- W2080992495 hasLocation W20809924953 @default.
- W2080992495 hasLocation W20809924954 @default.
- W2080992495 hasLocation W20809924955 @default.
- W2080992495 hasOpenAccess W2080992495 @default.
- W2080992495 hasPrimaryLocation W20809924951 @default.
- W2080992495 hasRelatedWork W2003465964 @default.
- W2080992495 hasRelatedWork W2057623054 @default.
- W2080992495 hasRelatedWork W2317200988 @default.
- W2080992495 hasRelatedWork W2371447506 @default.
- W2080992495 hasRelatedWork W2376932109 @default.
- W2080992495 hasRelatedWork W2386767533 @default.
- W2080992495 hasRelatedWork W2748952813 @default.
- W2080992495 hasRelatedWork W2899084033 @default.
- W2080992495 hasRelatedWork W3107474891 @default.
- W2080992495 hasRelatedWork W4225307033 @default.
- W2080992495 hasVolume "2007" @default.
- W2080992495 isParatext "false" @default.
- W2080992495 isRetracted "false" @default.
- W2080992495 magId "2080992495" @default.
- W2080992495 workType "article" @default.