Computer modelling in tomography and ill-posed problems /

Computer modelling in tomography and ill-posed problems /

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Bibliographic Details
Main Authors: Lavrentʹev, M. M. (Mikhail Mikhaĭlovich) (Author), Zerkal, S. M. (Author), Trofimov, O. E. (Oleg Evgenʹevich) (Author)
Format: Electronic eBook
Language:English
Published: Utrecht ; Boston : VSP, 2001.
Series:Inverse and ill-posed problems series.
Subjects:
Geometric tomography.
Inverse problems (Differential equations)
Electronic books.
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.

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