Mathematical Methods in Image Reconstruction
Seiten
2006
Society for Industrial & Applied Mathematics,U.S. (Verlag)
978-0-89871-622-1 (ISBN)
Society for Industrial & Applied Mathematics,U.S. (Verlag)
978-0-89871-622-1 (ISBN)
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Describes the state of the art of the mathematical theory and numerical analysis of imaging. The authors survey and provide a unified view of imaging techniques, provide the necessary mathematical background and common framework, and give a detailed analysis of the numerical algorithms.
Since the advent of computerized tomography in radiology, many imaging techniques have been introduced in medicine, science, and technology. This book describes the state of the art of the mathematical theory and numerical analysis of imaging. The authors survey and provide a unified view of imaging techniques, provide the necessary mathematical background and common framework, and give a detailed analysis of the numerical algorithms. This book not only reflects the theoretical progress and the growth of the field in the last 10 years but also serves as an excellent reference. It will provide readers with a superior understanding of the mathematical principles behind imaging and will enable them to write state-of-the-art software as a result.
Mathematical Methods in Image Reconstruction provides a very detailed description of two-dimensional algorithms. For three-dimensional algorithms, the authors derive exact and approximate inversion formulas for specific imaging devices and describe their algorithmic implementation (which by and large parallels the two-dimensional algorithms). Integral geometry is surveyed as far as is necessary for imaging purposes; imaging techniques based on or related to integral geometry are briefly described in the section on tomography.
Some of the applications covered in the book include computerized tomography, magnetic resonance imaging, emission tomography, electron microscopy, ultrasound transmission tomography, industrial tomography, seismic tomography, impedance tomography, and NIR imaging. The authors provide the necessary mathematical background and common mathematical framework needed to understand the book. Knowledge of tomography literature from the 1980s will be useful to the reader.
Since the advent of computerized tomography in radiology, many imaging techniques have been introduced in medicine, science, and technology. This book describes the state of the art of the mathematical theory and numerical analysis of imaging. The authors survey and provide a unified view of imaging techniques, provide the necessary mathematical background and common framework, and give a detailed analysis of the numerical algorithms. This book not only reflects the theoretical progress and the growth of the field in the last 10 years but also serves as an excellent reference. It will provide readers with a superior understanding of the mathematical principles behind imaging and will enable them to write state-of-the-art software as a result.
Mathematical Methods in Image Reconstruction provides a very detailed description of two-dimensional algorithms. For three-dimensional algorithms, the authors derive exact and approximate inversion formulas for specific imaging devices and describe their algorithmic implementation (which by and large parallels the two-dimensional algorithms). Integral geometry is surveyed as far as is necessary for imaging purposes; imaging techniques based on or related to integral geometry are briefly described in the section on tomography.
Some of the applications covered in the book include computerized tomography, magnetic resonance imaging, emission tomography, electron microscopy, ultrasound transmission tomography, industrial tomography, seismic tomography, impedance tomography, and NIR imaging. The authors provide the necessary mathematical background and common mathematical framework needed to understand the book. Knowledge of tomography literature from the 1980s will be useful to the reader.
Frank Natterer is a Professor in the Institut für Numerische und instrumentelle Mathematik at the University of Münster. Frank Wübbeling is a researcher in the Institut für Numerische und instrumentelle Mathematik at the University of Münster.
Chapter 1: Introduction
Chapter 2: Integral Geometry
Chapter 3: Tomography
Chapter 4: Stability and Resolution
Chapter 5: Reconstruction Algorithms
Chapter 6: Problems That Have Peculiarities
Chapter 7: Nonlinear Tomography.
| Erscheint lt. Verlag | 13.9.2007 |
|---|---|
| Reihe/Serie | Mathematical Modeling and Computation |
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 152 x 229 mm |
| Gewicht | 420 g |
| Themenwelt | Informatik ► Grafik / Design ► Digitale Bildverarbeitung |
| Mathematik / Informatik ► Informatik ► Theorie / Studium | |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Technik | |
| ISBN-10 | 0-89871-622-5 / 0898716225 |
| ISBN-13 | 978-0-89871-622-1 / 9780898716221 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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