Geodesic
Reconstruction of a function and its singular support in a cylinder by tomographic data
Eurasian journal of mathematical and computer applications, Tome 8 (2020) no. 2, pp. 86-97

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In this article we consider problems of reconstruction of a function and its singular support by using tomographic data. The data for the problems are values of the attenuated geodesic x-ray transform which is a set of integrals of an unknown function calculated along geodesics of the Riemannian metric that is used for modelling refraction in a cylinder. The values of the attenuated geodesic x-ray transform are received in a slice-by-slice fan-beam scheme. Our approach is based on the slice-by-slice reconstruction of the sought-for function or its singular support using a modification of well-known operators of back-projection and break indicator.
Keywords: Tomography, refraction, absorption, attenuated geodesic x-ray transform, Riemannian metric, singular support. 
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     author = {S. V. Mal'tseva and I. E. Svetov and A. P. Polyakova},
     title = {Reconstruction of a function and its singular support in a cylinder by tomographic data},
     journal = {Eurasian journal of mathematical and computer applications},
     pages = {86--97},
     publisher = {mathdoc},
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     number = {2},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJMCA_2020_8_2_a5/}
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S. V. Mal'tseva; I. E. Svetov; A. P. Polyakova. Reconstruction of a function and its singular support in a cylinder by tomographic data. Eurasian journal of mathematical and computer applications, Tome 8 (2020) no. 2, pp. 86-97. http://geodesic.mathdoc.fr/item/EJMCA_2020_8_2_a5/