Computer modelling in tomography and ill-posed problems / M.M. Lavrentèv, S.M. Zerkal and O.E. Trofimov.
- Reprint 2014
- Utrecht ; Boston : VSP, 2001.
- Inverse and ill-posed problems series.
Inverse and ill-posed problems series
1 online resource (136 pages) : illustrations.
- Geometric tomography.
Inverse problems (Differential equations).
- Electronic books.
- Comparatively weakly researched untraditional tomography problems are solved because of new achievements in calculation mathematics and the theory of ill-posed problems, the regularization process of solving ill-posed problems, and the increase of stability. Experiments show possibilities and applicability of algorithms of processing tomography data. This monograph is devoted to considering these problems in connection with series of ill-posed problems in tomography settings arising from practice.The book includes chapters to the following themes: Mathematical basis of the method of computerized tomography Cone-beam tomography reconstruction Inverse kinematic problem in the tomographic setting
- Machine generated contents note: Chapter 1. Mathematical basis of the method of computerized
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
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
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
- Bibliographic Level Mode of Issuance: Monograph
Includes bibliographical references.
Description based on print version record.
- Zerkal, S. M., author.
Trofimov, O. E. (Oleg Evgenʹevich), author.
- Publisher Number:
- 10.1515/9783110940930 doi
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