Description 
1 online resource (136 pages) : illustrations 
Series 
Inverse and illposed problems series 

Inverse and illposed 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 illposed problems11  1.2. Problem of integral geometry16  1.3. The Radon transform18  1.4. Radon problem as an example of an illposed problem20  1.5. The algorithm of inversion of the twodimensional Radon  transform based on the convolution with the generalized  function l/z225  Chapter 2. Conebeam tomography reconstruction 33  2.1. Reducing the inversion formulas of conebeam 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 threedimensional 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  threedimensional 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 (ebook) 

9783110940930 (ebook) 
