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

Format:

Book

Author/Creator:

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

Zerkal, S. M., author.

Trofimov, O. E. (Oleg Evgenʹevich), author.

Series:

Inverse and ill-posed problems series.

Inverse and ill-posed problems series

Language:

English

Subjects (All):

Geometric tomography.

Inverse problems (Differential equations).

Physical Description:

1 online resource (136 pages) : illustrations.

Edition:

Reprint 2014

Place of Publication:

Utrecht ; Boston : VSP, 2001.

Language Note:

English

Summary:

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

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.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references.

Description based on print version record.

ISBN:

9783110940930

3110940930

OCLC:

1013949647