Inversion of the scalar and vector attenuated X-ray transforms in a unit disc
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S. G. Kazantsev
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.
© de Gruyter
Articles in the same Issue
- Inverse problems of plane wave scattering by 1D inhomogeneous layers
- Explicit representation for the solution to a parabolic differential identification problem in a Banach space
- Sensitivity functions and their uses in inverse problems
- Identification problems for parabolic delay differential equations with measurement on the boundary
- Inversion of the scalar and vector attenuated X-ray transforms in a unit disc
Articles in the same Issue
- Inverse problems of plane wave scattering by 1D inhomogeneous layers
- Explicit representation for the solution to a parabolic differential identification problem in a Banach space
- Sensitivity functions and their uses in inverse problems
- Identification problems for parabolic delay differential equations with measurement on the boundary
- Inversion of the scalar and vector attenuated X-ray transforms in a unit disc
