Introduction to the Mathematics of Medical Imaging

by Epstein. Charles L.

• ISBN13: 9780898716429
• ISBN10: 089871642X
• Edition: 2nd
• Format: Paperback
• Copyright: 2007-09-28
• Publisher: Society for Industrial & Applied

Summary

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.

Author Biography

Charles L. Epstein is a Professor at the University of Pennsylvania with appointments in mathematics and radiology. He works in numerical analysis, magnetic resonance imaging, and image analysis, and has also worked in a variety of fields of mathematical analysis connected to partial differential equations and several complex variables. Professor Epstein is on the editorial board of Inverse Problems and he is an editor of BirkhSuser's Cornerstones book series.

Table of Contents

Preface to the second edition

Preface

How to use this nook

Notational conventions

Measurements and modeling

Linear models and linear equations

A basic model for tomography

Introduction to the Fourier transform

Convolution

The radon transform

Introduction to Fourier series

Sampling

Filters

Implementing shift invariant filters

Reconstruction in X-ray tomography

Imaging artifacts in X-ray tomography

Algebraic reconstruction techniques

Magnetic resonance imaging

Probability and random variables

Applications of probability

Random processes

Background material

Basic analysis

Bibliography

Index

Table of Contents provided by Publisher. All Rights Reserved.