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Computer modelling in tomography and ill-posed problems / / M.M. Lavrentèv, S.M. Zerkal and O.E. Trofimov
| Computer modelling in tomography and ill-posed problems / / M.M. Lavrentèv, S.M. Zerkal and O.E. Trofimov |
| Autore | Lavrentʹev M. M (Mikhail Mikhaĭlovich) |
| Edizione | [Reprint 2014] |
| Pubbl/distr/stampa | Utrecht ; ; Boston : , : VSP, , 2001 |
| Descrizione fisica | 1 online resource (136 pages) : illustrations |
| Disciplina | 516 |
| Collana | Inverse and ill-posed problems series |
| Soggetto topico |
Geometric tomography
Inverse problems (Differential equations) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 3-11-094093-0 |
| Classificazione | ST 640 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 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. |
| Record Nr. | UNINA-9910463726303321 |
Lavrentʹev M. M (Mikhail Mikhaĭlovich)
|
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| Utrecht ; ; Boston : , : VSP, , 2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Computer modelling i...
Computer modelling in tomography and ill-posed problems / / M.M. Lavrentèv, S.M. Zerkal and O.E. Trofimov
| Computer modelling in tomography and ill-posed problems / / M.M. Lavrentèv, S.M. Zerkal and O.E. Trofimov |
| Autore | Lavrentʹev M. M (Mikhail Mikhaĭlovich) |
| Edizione | [Reprint 2014] |
| Pubbl/distr/stampa | Utrecht ; ; Boston : , : VSP, , 2001 |
| Descrizione fisica | 1 online resource (136 pages) : illustrations |
| Disciplina | 516 |
| Collana | Inverse and ill-posed problems series |
| Soggetto topico |
Geometric tomography
Inverse problems (Differential equations) |
| Soggetto non controllato |
Algorithms
Calculation Mathematics Cone-beam Ill-posed Problems Inverse Kinematic Problem Regularization Tomography |
| ISBN | 3-11-094093-0 |
| Classificazione | ST 640 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 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. |
| Record Nr. | UNINA-9910788955503321 |
|
Lavrentʹev M. M (Mikhail Mikhaĭlovich)
|
||
| Utrecht ; ; Boston : , : VSP, , 2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Computer modelling i...
Computer modelling in tomography and ill-posed problems / / M.M. Lavrentèv, S.M. Zerkal and O.E. Trofimov
| Computer modelling in tomography and ill-posed problems / / M.M. Lavrentèv, S.M. Zerkal and O.E. Trofimov |
| Autore | Lavrentʹev M. M (Mikhail Mikhaĭlovich) |
| Edizione | [Reprint 2014] |
| Pubbl/distr/stampa | Utrecht ; ; Boston : , : VSP, , 2001 |
| Descrizione fisica | 1 online resource (136 pages) : illustrations |
| Disciplina | 516 |
| Collana | Inverse and ill-posed problems series |
| Soggetto topico |
Geometric tomography
Inverse problems (Differential equations) |
| Soggetto non controllato |
Algorithms
Calculation Mathematics Cone-beam Ill-posed Problems Inverse Kinematic Problem Regularization Tomography |
| ISBN | 3-11-094093-0 |
| Classificazione | ST 640 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 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. |
| Record Nr. | UNINA-9910813739403321 |
|
Lavrentʹev M. M (Mikhail Mikhaĭlovich)
|
||
| Utrecht ; ; Boston : , : VSP, , 2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Computer modelling i...