Mathematical Methods in Image Reconstruction

This book provides readers with a superior understanding of the mathematical principles behind imaging.

Frank Natterer (Author), Frank Wübbeling (Author)

9780898716221, Society for Industrial and Applied Mathematics

Paperback / softback, published 30 April 2006

228 pages
22.9 x 15.2 x 2 cm, 0.42 kg

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. 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.

1. Introduction
2. Integral geometry
3. Tomography
4. Stability and resolution
5. Reconstruction algorithms
6. Problems that have peculiarities
7. Nonlinear tomography.

Subject Areas: Miscellaneous items [WZ]