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Inversion of the Radon transform, based on the theory of A-analytic functions, with application to 3D inverse kinematic problem with local data
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A. L. Bukhgeim
Veröffentlicht/Copyright:
2006
In the introduction we show that the inverse problems for transport equations are naturally reduced to the Cauchy problem for the so called A-analytic functions, and hence the solution is given in terms of operator analog of the Cauchy transform. In Section 2 we develop elements of the theory of A-analytic functions and obtain stability estimates for our Cauchy transform. In Section 3 we discuss numerical aspects of this transformation. In Section 4 we apply this algorithm to the 3-dimensional inverse kinematic problem with local data on the Earth surface, using modified Newton method and discuss numerical examples.
Published Online: --
Published in Print: 2006-05-01
Copyright 2006, Walter de Gruyter
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- Inversion of the Radon transform, based on the theory of A-analytic functions, with application to 3D inverse kinematic problem with local data
- An identification problem arising in the theory of heat conduction for materials with memory
- On the choice of the regularization parameter in ill-posed problems with approximately given noise level of data
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Artikel in diesem Heft
- Inversion of the Radon transform, based on the theory of A-analytic functions, with application to 3D inverse kinematic problem with local data
- An identification problem arising in the theory of heat conduction for materials with memory
- On the choice of the regularization parameter in ill-posed problems with approximately given noise level of data
- An iterative method for reconstruction of temperature
- Boundary data identification for a eddy-current problem on polyhedra: numerical approach
- Inverse scattering problem for two-dimensional Schrödinger operator
- Motion estimation by hybrid diffusion: theory and implementation
