Fourier Methods in Imaging
2nd Edition
Published on 21. May 2010
Book
Hardback
954 pages
978-0-470-68983-7 (ISBN)
Description
Fourier Methods in Imaging introduces the mathematical tools for modeling linear imaging systems to predict the action of the system or for solving for the input. The chapters are grouped into five sections, the first introduces the imaging "tasks" (direct, inverse, and system analysis), the basic concepts of linear algebra for vectors and functions, including complex-valued vectors, and inner products of vectors and functions. The second section defines "special" functions, mathematical operations, and transformations that are useful for describing imaging systems. Among these are the Fourier transforms of 1-D and 2-D function, and the Hankel and Radon transforms. This section also considers approximations of the Fourier transform. The third and fourth sections examine the discrete Fourier transform and the description of imaging systems as linear "filters", including the inverse, matched, Wiener and Wiener-Helstrom filters. The final section examines applications of linear system models to optical imaging systems, including holography.
* Provides a unified mathematical description of imaging systems.
* Develops a consistent mathematical formalism for characterizing imaging systems.
* Helps the reader develop an intuitive grasp of the most common mathematical methods, useful for describing the action of general linear systems on signals of one or more spatial dimensions.
* Offers parallel descriptions of continuous and discrete cases.
* Includes many graphical and pictorial examples to illustrate the concepts.
This book helps students develop an understanding of mathematical tools for describing general one- and two-dimensional linear imaging systems, and will also serve as a reference for engineers and scientists
Reviews / Votes
"Overall, this is an excellent text, appropriate for the graduate student approaching this material for the first time, and for the seasoned professional looking for an up-to-date reference." (Journal of Electronic Imaging, 1 April 2011) "This comprehensive textbook represents a practical review of Fourier techniques in imaging methods. It will be very useful for graduate students (in engineering, science, computer science, and applied mathematics) as well as engineers interested in linear imaging systems." (Zentralblatt Math, 2010)More details
Series
Edition
2. Auflage
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Product notice
sewn/stitched
Paper over boards
Dimensions
Height: 250 mm
Width: 175 mm
Thickness: 55 mm
Weight
1795 gr
ISBN-13
978-0-470-68983-7 (9780470689837)
Schweitzer Classification
Other editions
Additional editions
Roger L. Easton Jr.
Fourier Methods in Imaging
E-Book
11/2010
2nd Edition
Wiley
€134.99
Available for download
Roger L. Easton Jr.
Fourier Methods in Imaging
E-Book
03/2010
2nd Edition
Wiley
€134.99
Available for download
Person
Professor Roger L. Easton, Jr
Chester F. Carlson Center for Imaging Science, Rochester Institute of Technology
Professor Easton teaches undergraduate and graduate courses in linear systems, optical imaging, and digital image processing at Rochester Institute of Technology. He received a B.S. degree in Astronomy from Haverford College, an M.S. in physics from the University of Maryland, and an M.S. and Ph.D. degree in Optical Sciences from the University of Arizona.
His research interests include the application of digital image processing to text documents and manuscripts. He has contributed to work on the Dead Sea Scrolls and is now part of an imaging team helping scolars to read the original Archimiedes Palimpsest. Professor Easton also conducts research into optical signal processing and computer-generated holography, publishing articles on both.
Chester F. Carlson Center for Imaging Science, Rochester Institute of Technology
Professor Easton teaches undergraduate and graduate courses in linear systems, optical imaging, and digital image processing at Rochester Institute of Technology. He received a B.S. degree in Astronomy from Haverford College, an M.S. in physics from the University of Maryland, and an M.S. and Ph.D. degree in Optical Sciences from the University of Arizona.
His research interests include the application of digital image processing to text documents and manuscripts. He has contributed to work on the Dead Sea Scrolls and is now part of an imaging team helping scolars to read the original Archimiedes Palimpsest. Professor Easton also conducts research into optical signal processing and computer-generated holography, publishing articles on both.
Content
Series Editor's Preface
Preface
1 Introduction
2 Operators and Functions
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Vectors with Real-Valued Components
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 Complex Numbers and Functions
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Complex-Valued Matrices and Systems
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 1-D Special Functions
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7 2-D Special Functions
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8 Linear Operators
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9 Fourier Transforms of 1-D Functions
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10 Multidimensional Fourier Transforms
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11 Spectra of Circular Functions
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12 The Radon Transform
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13 Approximations to Fourier Transforms 13.1 Moment Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14 Discrete Systems, Sampling, and Quantization
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15 Discrete Fourier Transforms 511
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16 Magnitude Filtering
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17 Allpass (Phase) Filters
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18 Magnitude-Phase Filters
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19 Applications of Linear Filters
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20 Filtering in Discrete Systems
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21 Optical Imaging in Monochromatic Light
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22 Incoherent Optical Imaging Systems
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23 Holography
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References
Index