Computer modelling in tomography and ill-posed problems /
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| Main Authors: | , , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Utrecht ; Boston :
VSP,
2001.
|
| Series: | Inverse and ill-posed problems series.
|
| Subjects: | |
| Online Access: | An electronic book accessible through the World Wide Web; click to view |
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Table of Contents:
- Machine generated contents note: Chapter 1. Mathematical basis of the method of computerized
- tomography 11
- 1.1. Basic notions of the theory of ill-posed problems11
- 1.2. Problem of integral geometry16
- 1.3. The Radon transform18
- 1.4. Radon problem as an example of an ill-posed problem20
- 1.5. The algorithm of inversion of the two-dimensional Radon
- transform based on the convolution with the generalized
- function l/z225
- Chapter 2. Cone-beam tomography reconstruction 33
- 2.1. Reducing the inversion formulas of cone-beam tomography recont
- struction to the form convenient for constructing numerical
- algorithm s33
- 2.2. Elements of the theory of generalized functions in application to
- problems of inversion of the ray transformation45
- 2.3. The relations between the Radon, Fourier,
- and ray transformations51
- Chapter 3. Inverse kinematic problem
- in the tomographic setting 55
- 3.1. Direct kinematic problem and numerical solution
- for three-dimensional regular media55
- 3.2. Formulation of the inverse kinematic problem with the use of
- a tomography system of data gathering66
- 3.3. Deduction of the basic inversion formula and the algorithm of
- solving the inverse kinematic problem in
- three-dimensional linearized formulation68
- 3.4. Model experiment and numerical study of the algorithm79
- 3.5. Solution of the inverse kinematic problem by the method of
- computerized tomography for media with opaque inclusions 98
- Appendix: Reconstruction with the use
- of the standard model 112
- Bibliography 119.