The Mathematics of Computerized Tomography

Frank Natterer9780898714937, 0898714931

This book provides a unified view of tomographic techniques, a common mathematical framework, and an in-depth treatment of reconstruction algorithms. It focuses on the reconstruction of a function from line or plane integrals, with special emphasis on applications in radiology, science, and engineering. The Mathematics of Computerized Tomography covers the relevant mathematical theory of the Radon transform and related transforms and also studies more practical questions such as stability, sampling, resolution, and accuracy. Quite a bit of attention is given to the derivation, analysis, and practical examination of reconstruction algorithms, for both standard problems and problems with incomplete data.
Audience: Applied mathematicians, physicists, and engineers working in image reconstruction will find this book particularly useful.

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Table of contents :
The Mathematics of Computerized Tomography……Page 2
ISBN 0-89871-493-1……Page 7
Contents……Page 8
Preface to the Classics Edition……Page 10
Preface……Page 12
Glossary of Symbols……Page 14
Errata……Page 16
I Computerized Tomography……Page 20
II The Radon Transform and Related Transforms……Page 28
III Sampling and Resolution……Page 73
IV Ill-posedness and Accuracy……Page 104
V Reconstruction Algorithms……Page 121
VI Incomplete Data……Page 177
VII Mathematical Tools……Page 203
References……Page 236
Index……Page 244