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- W2011016066 abstract "The x-ray transform I associates with a covariant symmetric tensor field f(x) of order , the line function If(l) by integration over the line l. In this paper, new reconstruction formulae for the solenoidal part of f are obtained. The case when If is known only for the family of lines intersecting a given curve in is considered as well. The formulae obtained contain only a finite number of differentiations, integrations, solving of linear algebraic equations and application the Laplacian powers. The formulae are obtained under the assumption that every plane intersecting the support of f intersects the curve m + 1 times. It is shown that the number of intersection points cannot be decreased. It is shown that the similar considerations are valid for two other admissible families of lines in : lines parallel to a given curve of directions and lines tangential to a given surface." @default.
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- W2011016066 date "2006-02-13" @default.
- W2011016066 modified "2023-09-27" @default.
- W2011016066 title "Inversion of the x-ray transform for 3D symmetric tensor fields with sources on a curve" @default.
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- W2011016066 doi "https://doi.org/10.1088/0266-5611/22/2/001" @default.
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