Geodesic
Reconstruction of a vector field from the data of its longitudinal and transverse ray transforms
Daghestan Electronic Mathematical Reports, no. 16 (2021), pp. 62-73 Cet article a éte moissonné depuis la source Math-Net.Ru

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An algorithm for the complete reconstruction of a vector field in three-dimensional Euclidean space based on incomplete integral data of a longitudinal and a transverse ray transforms is constructed. From of data of a longitudinal ray transform given on the family of straight lines intersecting a piecewise smooth curve, the solenoidal part of the vector field is constructed, and from of data of a transverse ray transform, the potential of an unknown field is constructed. The problem of reconstruction is also solved in the case of a family of lines intersecting a curve at infinity.
Mots-clés : Radon transformation, transverse ray transform, inversion formula.
Keywords: longitudinal ray transform 
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     author = {Z. G. Medzhidov},
     title = {Reconstruction of a vector field from the data of its longitudinal and transverse ray transforms},
     journal = {Daghestan Electronic Mathematical Reports},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DEMR_2021_16_a4/}
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Z. G. Medzhidov. Reconstruction of a vector field from the data of its longitudinal and transverse ray transforms. Daghestan Electronic Mathematical Reports, no. 16 (2021), pp. 62-73. http://geodesic.mathdoc.fr/item/DEMR_2021_16_a4/

[1] Palamodov V.P., “On reconstruction of strain fields from tomographic data”, ID 85002, Inverse Problems, 31:8 (2015), 12 | DOI | MR | Zbl

[2] Palamodov V.P., “Reconstruction of a differential form from Doppler transform”, SIAM J. Math. Anal, 2009, no. 41, 1713–1720 | DOI | MR | Zbl

[3] Medzhidov Z.G., “Obraschenie luchevogo preobrazovaniya tenzornykh polei s beskonechno udalennymi istochnikami”, Vestnik DGU, 2015, no. 1, 19-26

[4] Medzhidov Z.G., “Formuly obrascheniya tenzornoi tomografii po nepolnym dannym”, DEMI, 2014, no. 2, 75-86

[5] Medzhidov Z.G., “O vosstanovlenii tenzornogo polya vtorogo ranga s nulevym sledom po nepolnym dannym”, DEMI, 2020, no. 14, 38-47