Computer Modelling in Tomography and Ill-Posed Problems

✍ Scribed by Mikhail M. Lavrent'ev; Sergei M. Zerkal; Oleg E. Trofimov

Publisher: De Gruyter
Year: 2001
Tongue: English
Leaves: 136
Series: Inverse and Ill-Posed Problems Series; 27
Edition: Reprint 2014
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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

✦ Table of Contents

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

📜 SIMILAR VOLUMES

Computer Modelling in Tomography and Ill

📁 Computer Modelling in Tomography and Ill Posed Problems

✍ Michail M. Lavrent'ev; M. Mikhail Mikhailovich Lavrentev; S. M. Zerkal; Oleg Evg 📂 Library 📅 2001 🏛 VSP 🌐 English

The last decades of the 20th century were marked by the appearance of a new field of mathematics: computerized tomography. Its theory forms the basis for the solution of many applied problems. The methods of computerized tomography make it possible study the interior structure of a body by examining

Mathematical problems in computed tomogr

📁 Mathematical problems in computed tomography

✍ Faridani A. 📂 Library 📅 1999 🌐 English

Optimization Techniques in Computer Visi

📁 Optimization Techniques in Computer Vision: Ill-Posed Problems and Regularization

✍ Mongi A. Abidi, Andrei V. Gribok, Joonki Paik 📂 Library 📅 2016 🏛 Abidi, Mongi A., Gribok, Andrei V., Paik, Joonki., 🌐 English

This book presents practical optimization techniques used in image processing and computer vision problems. Ill-posed problems are introduced and used as examples to show how each type of problem is related to typical image processing and computer vision problems. Unconstrained optimization gives th

Optimization Techniques in Computer Visi

📁 Optimization Techniques in Computer Vision: Ill-Posed Problems and Regularization

✍ Mongi A. Abidi, Andrei V. Gribok, Joonki Paik (auth.) 📂 Library 📅 2016 🏛 Springer International Publishing 🌐 English

<p>This book presents practical optimization techniques used in image processing and computer vision problems. Ill-posed problems are introduced and used as examples to show how each type of problem is related to typical image processing and computer vision problems. Unconstrained optimization gives

Optimization Techniques in Computer Visi

📁 Optimization Techniques in Computer Vision. Ill-posed Problems and Regularization

✍ Mongi A. Abidi, Andrei V. Gribok, Joonki Paik 📂 Library 📅 2016 🏛 Springer 🌐 English

Operator Theory and Ill-Posed Problems:

📁 Operator Theory and Ill-Posed Problems: Posed Problems

✍ Lavrent'ev M.M., Savel'ev L.Ya. 📂 Library 📅 2006 🏛 VSP 🌐 English

This book consists of three major parts. The first two parts deal with general mathematical concepts and certain areas of operator theory. The third part is devoted to ill-posed problems. It can be read independently of the first two parts and presents a good example of applying the methods of calcu