Computer Modelling in Tomography and Ill-Posed Problems
1st Edition
Published on 18. February 2001
Book
Hardback
134 pages
978-90-6764-350-4 (ISBN)
Description
Comparatively weakly researched untraditional tomography problems aresolved 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
Mathematical basis of the method of computerized tomography Cone-beam tomography reconstruction Inverse kinematic problem in the tomographic setting
More details
Series
Language
English
Place of publication
Zeist
Netherlands
Publishing group
Brill
Target group
College/higher education
Professional and scholarly
US School Grade: College Graduate Student
Weight
355 gr
ISBN-13
978-90-6764-350-4 (9789067643504)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Mikhail M. Lavrent'ev | Sergei M. Zerkal | Oleg E. Trofimov
Computer Modelling in Tomography and Ill-Posed Problems
Book
08/2014
1st Edition
De Gruyter
€209.00
Withdrawn from sale
Mikhail M. Lavrent'ev | Sergei M. Zerkal | Oleg E. Trofimov
Computer Modelling in Tomography and Ill-Posed Problems
Basic Concepts and Protocols Implementation
E-Book
07/2014
1st Edition
De Gruyter
€149.95
Available for download
Mikhail M. Lavrent'ev | Sergei M. Zerkal | Oleg E. Trofimov
Computer Modelling in Tomography and Ill-Posed Problems
Book
02/2001
1st Edition
De Gruyter
€159.95
Shipment within 7-9 days
Persons
Mikhail M. Lavrent'ev ?; Sergei M. Zerkal, Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk, Russia; Oleg E. Trofimov, Institute of Automation and Electrometry, Russian Academy of Sciences, Novosibirsk, Russia.
Content
Introduction
MATHEMATICAL BASIS OF THE METHOD OF COMPUTERIZED TOMOGRAPHY
Basic notions of the theory of ill-posed problems
Problem of integral geometry
The Radon transfer
Radon problem as an example of an ill-posed problem
The algorithm of inversion of the two-dimensional Radon transform based on the convolution with the generalized function 1/z2
CONE-BEAM TOMOGRAPHY RECONSTRUCTION
Reducing the inversion formulas of cone-beam tomography reconstruction to the form convenient for constructing numerical algorithms
Elements of the theory of generalized functions in application to problems of inversion of the ray transformation
The relations between the Radon, Fourier and ray transformations
INVERSE KINEMATIC PROBLEM IN THE TOMOGRAPHIC SETTING
Direct kinematic problem and numerical solution for three-dimensional regular media
Formulation of the inverse kinematic problem with the use of a tomography system of data gathering
Deduction on the basic inversion formula and the algorithm of solving the inverse kinematic problem in three-dimensional linearized formulation
Model experiment and numerical study of the algorithm
Solution of the inverse kinematic problem by the method of computerized tomography for media with opaque inclusions
APPENDIX: RECONSTRUCTION WITH THE USE OF THE STANDARD MODEL
Bibliography
MATHEMATICAL BASIS OF THE METHOD OF COMPUTERIZED TOMOGRAPHY
Basic notions of the theory of ill-posed problems
Problem of integral geometry
The Radon transfer
Radon problem as an example of an ill-posed problem
The algorithm of inversion of the two-dimensional Radon transform based on the convolution with the generalized function 1/z2
CONE-BEAM TOMOGRAPHY RECONSTRUCTION
Reducing the inversion formulas of cone-beam tomography reconstruction to the form convenient for constructing numerical algorithms
Elements of the theory of generalized functions in application to problems of inversion of the ray transformation
The relations between the Radon, Fourier and ray transformations
INVERSE KINEMATIC PROBLEM IN THE TOMOGRAPHIC SETTING
Direct kinematic problem and numerical solution for three-dimensional regular media
Formulation of the inverse kinematic problem with the use of a tomography system of data gathering
Deduction on the basic inversion formula and the algorithm of solving the inverse kinematic problem in three-dimensional linearized formulation
Model experiment and numerical study of the algorithm
Solution of the inverse kinematic problem by the method of computerized tomography for media with opaque inclusions
APPENDIX: RECONSTRUCTION WITH THE USE OF THE STANDARD MODEL
Bibliography