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Introduction to the mathematics of medical imaging

Author: Charles L Epstein
Publisher: Philadelphia, PA : Society for Industrial and Applied Mathematics, ©2008.
Edition/Format:   Print book : English : 2nd edView all editions and formats
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 imaging modalities in current use. In the process, it also covers many important analytic  Read more...
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Additional Physical Format: Online version:
Epstein, Charles L.
Introduction to the mathematics of medical imaging.
Philadelphia, PA : Society for Industrial and Applied Mathematics, ©2008
(OCoLC)989691325
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Charles L Epstein
ISBN: 9780898716429 089871642X
OCLC Number: 156845912
Description: xxxiii, 761 pages : illustrations ; 26 cm
Contents: 1. Measurements and Modeling --
2. Linear Models and Linear Equations --
3. A Basic Model for Tomography --
4. Introduction to the Fourier Transform --
5. Convolution --
6. The Radon Transform --
7. Introduction to Fourier Series --
8. Sampling --
9. Filters --
10. Implementing Shift Invariant Filters --
11. Reconstruction in X-Ray Tomography --
12. Imaging Artifacts in X-Ray Tomography --
13. Algebraic Reconstruction Techniques --
14. Magnetic Resonance Imaging --
15. Probability and Random Variables --
16. Applications of Probability --
17. Random Processes --
A. Background Material --
B. Basic Analysis.
Responsibility: Charles L. Epstein.
More information:

Abstract:

"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, as well as 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." "The book is appropriate for one- or two-semester courses at the advanced undergraduate or beginning graduate level on the mathematical foundations of modern medical imaging technologies. The text assumes an understanding of calculus, linear algebra, and basic mathematical analysis."--Jacket.

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