Introduction to the Mathematics of Medical Imaging

Charles L. Epstein

ISBN 10: 089871642X / ISBN 13: 9780898716429

Published by Society for Industrial and Applied Mathematics,U.S., US, 2007

About this Item

At the heart of every medical imaging technology is a sophisticated mathematical model of the measurement process and an algorithm to reconstruct an image from the measured data. This book provides a firm foundation in the mathematical tools used to model the measurements and derive the reconstruction algorithms used in most imaging modalities in current use. In the process, it also covers many important analytic concepts, and techniques used in Fourier analysis, integral equations, sampling theory, and noise analysis.This text uses X-ray computed tomography as a ""pedagogical machine"" to illustrate important ideas and incorporates extensive discussions of background material making the more advanced mathematical topics accessible to readers with a less formal mathematical education. The mathematical concepts are illuminated with over 200 illustrations and numerous exercises.New to the second edition are a chapter on magnetic resonance imaging (MRI), a revised section on the relationship between the continuum and discrete Fourier transforms, a new section on Grangreat's formula, an improved description of the gridding method, and a new section on noise analysis in MRI.

Seller Inventory # LU-9780898716429

Bibliographic Details

• Title: Introduction to the Mathematics of Medical Imaging
• Publisher: Society for Industrial and Applied Mathematics,U.S., US
• Publication Date: 2007
• Language: English
• ISBN 10: 089871642X
• ISBN 13: 9780898716429
• Binding: Paperback
• Edition: Second Edition.
• Condition: New
• Weight: 1318 grams

About this title

Synopsis

At the heart of every medical imaging technology is a sophisticated mathematical model of the measurement process and an algorithm to reconstruct an image from the measured data. This book provides a firm foundation in the mathematical tools used to model the measurements and derive the reconstruction algorithms used in most of these modalities. The text uses X-ray computed tomography (X-ray CT) as a 'pedagogical machine' to illustrate important ideas and its extensive discussion of background material makes the more advanced mathematical topics accessible to people with a less formal mathematical education. This new edition contains a chapter on magnetic resonance imaging (MRI), a revised section on the relationship between the continuum and discrete Fourier transforms, an improved description of the gridding method, and new sections on both Grangreat's formula and noise analysis in MR-imaging. Mathematical concepts are illuminated with over 200 illustrations and numerous exercises.

About the Author

Charles L. Epstein is a Professor at the University of Pennsylvania with appointments in Mathematics and Radiology.