Inversion of the scalar and vector attenuated X-ray transforms in a unit disc Full article
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Journal of Inverse and Ill-Posed Problems
ISSN: 0928-0219 , E-ISSN: 1569-3945 |
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| Output data | Year: 2007, Volume: 15, Number: 7, Pages: 735-765 Pages count : 31 DOI: 10.1515/jiip.2007.040 | ||||
| Tags | A-analytic functions; attenuated X-ray transform; attenuated vectorial X-ray transform; Radon transform; transport equation; Hilbert transform | ||||
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Abstract:
This paper summarizes some of the old results obtained for the problems of inverting the two-dimensional attenuated X-ray transform and the attenuated vectorial X-ray transform, both using the fan-beam geometry. These inverse problems are considered on the language of the transport equation and two approaches are described for solving them. The first one, dating back to 1996, gives the inversion formulae on the basis of the theory of so-called A-analytic functions. And the second method (developed by the authors in 2002) yields the inversion formulae for the scalar and vector attenuated X-ray transforms without using the theory of A-analytic functions, but merely by reducing the arising inverse problems to the unattenuated case by the change of variables. Numerical implementation details are also provided.
Cite:
Kazantsev S.G.
, Bukhgeim A.A.
Inversion of the scalar and vector attenuated X-ray transforms in a unit disc
Journal of Inverse and Ill-Posed Problems. 2007. V.15. N7. P.735-765. DOI: 10.1515/jiip.2007.040 Scopus OpenAlex
Inversion of the scalar and vector attenuated X-ray transforms in a unit disc
Journal of Inverse and Ill-Posed Problems. 2007. V.15. N7. P.735-765. DOI: 10.1515/jiip.2007.040 Scopus OpenAlex
Identifiers:
| Scopus: | 2-s2.0-38649122400 |
| OpenAlex: | W2044040194 |