
Mathematical Methods in Image Reconstruction
Society for Industrial & Applied Mathematics,U.S. (Publisher)
Published on 30. April 2006
Book
Paperback/Softback
228 pages
978-0-89871-622-1 (ISBN)
Description
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.
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.
More details
Series
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Product notice
Paperback (trade)
Unsewn / adhesive bound
Dimensions
Height: 254 mm
Width: 179 mm
Thickness: 15 mm
Weight
420 gr
ISBN-13
978-0-89871-622-1 (9780898716221)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
Frank Natterer is a Professor in the Institut fuer Numerische und instrumentelle Mathematik at the University of Muenster. Frank Wuebbeling is a researcher in the Institut fuer Numerische und instrumentelle Mathematik at the University of Muenster.
Content
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.
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.