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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{EJMCA_2020_8_2_a5,
     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},
     volume = {8},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJMCA_2020_8_2_a5/}
}
TY  - JOUR
AU  - S. V. Mal'tseva
AU  - I. E. Svetov
AU  - A. P. Polyakova
TI  - Reconstruction of a function and its singular support in a cylinder by tomographic data
JO  - Eurasian journal of mathematical and computer applications
PY  - 2020
SP  - 86
EP  - 97
VL  - 8
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJMCA_2020_8_2_a5/
LA  - en
ID  - EJMCA_2020_8_2_a5
ER  - 
%0 Journal Article
%A S. V. Mal'tseva
%A I. E. Svetov
%A A. P. Polyakova
%T Reconstruction of a function and its singular support in a cylinder by tomographic data
%J Eurasian journal of mathematical and computer applications
%D 2020
%P 86-97
%V 8
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJMCA_2020_8_2_a5/
%G en
%F EJMCA_2020_8_2_a5
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/