Geodesic
Momentum ray transforms over planar tensor fields
Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 3, pp. 26-41.

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The paper considers ray transforms over the moments of symmetric tensor fields of arbitrary rank given in the unit circle. The basic geometric and differential properties of mixed ray transforms over tensor fields and mixed ray transforms over moments of tensor fields are established. A simple algorithm for reconstructing a low-rank tensor field from known mixed ray transforms of its moments is proposed and justified.
Keywords: tensor field, mixed ray momentum transform, geometric properties, differential properties
Mots-clés : Radon transform, reconstruction algorithm. 
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E. Yu. Derevtsov. Momentum ray transforms over planar tensor fields. Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 3, pp. 26-41. http://geodesic.mathdoc.fr/item/SJIM_2023_26_3_a2/

[1] Deans S., The Radon Transform and Some of its Applications, Wiley, N. Y., 1983 | MR | Zbl

[2] Derevtsov E.Yu., Svetov I.E., “Tomography of tensor fields in the plane”, Eurasian J. Math. Comput. Appl., 3:2 (2015), 24–68

[3] Sharafutdinov V.A., Integral Geometry of Tensor Fields, VSP, Urtecht, 1994 | MR

[4] Derevtsov E.Yu., “Some problems of non-scalar tomography”, Sib. Elektron. Mat. Izv., 7 (2010), 81–111 (in Russian)

[5] Krishnan V.P., Manna R., Sahoo S.K., Sharafutdinov V.A., “Momentum ray transforms”, Inverse Probl. Imaging., 13:3 (2019), 679–701 | DOI | MR | Zbl

[6] Abhishek A., Mishra R.K., “Support theorems and an injectivity result for integral moments of a symmetric $m$-tensor field”, J. Fourier Anal. Appl., 25:4 (2019), 1487–1512 | DOI | MR

[7] Mishra R.K., “Full reconstruction of a vector field from restricted Doppler and first integral moment transforms in $R^{n}$”, J. Inverse Ill-Posed Probl., 28:2 (2020), 173–184 | DOI | MR | Zbl

[8] Mishra R.K., Sahoo S.K., “Injectivity and range description of first $(k+1)$ integral moment transforms over m-tensor fields in $R^{n}$”, SIAM J. Math. Anal., 53:1 (2021), 253–278 | DOI | MR | Zbl