Introduction

Chapter 1. Mathematical basis of the method of computerized tomography

1.1. Basic notions of the theory of ill-posed problems

1.2. Problem of integral geometry

1.3. The Radon transform

1.4. Radon problem as an example of an ill-posed problem

1.5. The algorithm of inversion of the two-dimensional Radon transform based on the convolution with the generalized function 1/z2

Chapter 2. Cone-beam tomography reconstruction

2.1. Reducing the inversion formulas of cone-beam tomography reconstruction to the form convenient for constructing numerical algorithms

2.2. Elements of the theory of generalized functions in application to problems of inversion of the ray transformation

2.3. The relations between the Radon, Fourier, and ray transformations

Chapter 3. Inverse kinematic problem in the tomographic setting

3.1. Direct kinematic problem and numerical solution for three-dimensional regular media

3.2. Formulation of the inverse kinematic problem with the use of a tomography system of data gathering

3.3. Deduction of the basic inversion formula and the algorithm of solving the inverse kinematic problem in three-dimensional linearized formulation

3.4. Model experiment and numerical study of the algorithm

3.5. 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