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Author Lavrentʹev, M. M. (Mikhail Mikhaĭlovich), author

Title Computer modelling in tomography and ill-posed problems / M.M. Lavrentèv, S.M. Zerkal and O.E. Trofimov
Published Utrecht ; Boston : VSP, 2001
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Description 1 online resource (136 pages) : illustrations
Series Inverse and ill-posed problems series
Inverse and ill-posed problems series.
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
Bibliography Includes bibliographical references
Notes Print version record
Subject Geometric tomography.
Inverse problems (Differential equations)
Form Electronic book
Author Trofimov, O. E. (Oleg Evgenʹevich), author
Zerkal, S. M., author
ISBN 3110940930 (e-book)
9783110940930 (e-book)