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The Resource Computer modelling in tomography and ill-posed problems, M.M. Lavrentèv, S.M. Zerkal and O.E. Trofimov

Computer modelling in tomography and ill-posed problems, M.M. Lavrentèv, S.M. Zerkal and O.E. Trofimov

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Author
Contributor
Language
eng
Work
Publication
Extent
1 online resource (136 pages)
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
Isbn
9783110940930
Link
http://libproxy.rpi.edu/login?url=https://ebookcentral.proquest.com/lib/connectny/detail.action?docID=3049437
Instance
Label
Computer modelling in tomography and ill-posed problems
Title
Computer modelling in tomography and ill-posed problems
Statement of responsibility
M.M. Lavrentèv, S.M. Zerkal and O.E. Trofimov
Creator
Contributor
Author
Subject
Language
eng
Member of
Cataloging source
MiAaPQ
Illustrations
illustrations
Index
no index present
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Inverse and ill-posed problems series
Computer modelling in tomography and ill-posed problems, M.M. Lavrentèv, S.M. Zerkal and O.E. Trofimov
Label
Computer modelling in tomography and ill-posed problems, M.M. Lavrentèv, S.M. Zerkal and O.E. Trofimov
Link
http://libproxy.rpi.edu/login?url=https://ebookcentral.proquest.com/lib/connectny/detail.action?docID=3049437
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Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type MARC source
rdacontent
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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http://library.link/vocab/discovery_link
{'f': 'http://opac.lib.rpi.edu/record=b4100253'}
Extent
1 online resource (136 pages)
Form of item
online
Isbn
9783110940930
Isbn Type
(e-book)
Media category
computer
Media MARC source
rdamedia
Other physical details
illustrations.
Sound
unknown sound
Specific material designation
remote

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