Image Science

1. VECTORS AND OPERATORS.
 
1.1 LINEAR VECTOR SPACES.
 
1.2 TYPES OF OPERATORS.
 
1.3 HILBERT-SPACE OPERATORS.
 
1.4 EIGENANALYSIS.
 
1.5 SINGULAR-VALUE DECOMPOSITION.
 
1.6 MOORE-PENROSE PSEUDOINVERSE.
 
1.7 PSEUDOINVERSES AND LINEAR EQUATIONS.
 
1.8 REPRODUCING-KERNEL HILBERT SPACES.
 
2. THE DIRAC DELTA AND OTHER GENERALIZED FUNCTIONS.
 
2.1 THEORY OF DISTRIBUTIONS.
 
2.2 ONE-DIMENSIONAL DELTA FUNCTION.
 
2.3 OTHER GENERALIZED FUNCTIONS IN 1D.
 
2.4 MULTIDIMENSIONAL DELTA FUNCTIONS.
 
3. FOURIER ANALYSIS.
 
3.1 SINES, COSINES AND COMPLEX EXPONENTIALS.
 
3.2 FOURIER SERIES.
 
3.3 1D FOURIER TRANSFORM.
 
3.4 MULTIDIMENSIONAL FOURIER TRANSFORMS.
 
3.5 SAMPLING THEORY.
 
3.6 DISCRETE FOURIER TRANSFORM.
 
4. SERIES EXPANSIONS AND INTEGRAL TRANSFORMS.
 
4.1 EXPANSIONS IN ORTHOGONAL FUNCTIONS.
 
4.2 CLASSICAL INTEGRAL TRANSFORMS.
 
4.3 FRESNEL INTEGRALS AND TRANSFORMS.
 
4.4 RADON TRANSFORM.
 
5. MIXED REPRESENTATIONS.
 
5.1 LOCAL SPECTRAL ANALYSIS.
 
5.2 BILINEAR TRANSFORMS.
 
5.3 WAVELETS.
 
6. GROUP THEORY.
 
6.1 BASIC CONCEPTS.
 
6.2 SUBGROUPS AND CLASSES.
 
6.3 GROUP REPRESENTATIONS.
 
6.4 SOME FINITE GROUPS.
 
6.5 CONTINUOUS GROUPS.
 
6.6 GROUPS OF OPERATORS ON A HILBERT SPACE.
 
6.7 QUANTUM MECHANICS AND IMAGE SCIENCE.
 
6.8 FUNCTIONS AND TRANSFORMS ON GROUPS.
 
7. DETERMINISTIC DESCRIPTIONS OF IMAGING SYSTEMS.
 
7.1 OBJECTS AND IMAGES.
 
7.2 LINEAR CONTINUOUS-TO-CONTINUOUS SYSTEMS.
 
7.3 LINEAR CONTINUOUS-TO-DISCRETE SYSTEMS.
 
7.4 LINEAR DISCRETE-TO-DISCRETE SYSTEMS.
 
7.5 NONLINEAR SYSTEMS.
 
8. STOCHASTIC DESCRIPTIONS OF OBJECTS AND IMAGES.
 
8.1 RANDOM VECTORS.
 
8.2 RANDOM PROCESSES.
 
8.3 NORMAL RANDOM VECTORS AND

HARRISON H. BARRETT received a BS in physics from Virginia Polytechnic Institute, an MS in Physics from MIT, and a PhD in applied physics from Harvard. Dr. Barrett is a professor in the Optical Sciences Center, the Department of Radiology, and the Program in Applied Mathematics and serves as Director of the Center for Gamma-ray Imaging. The holder of twenty-three U.S. patents, he is the recipient of the IEEE Medical Imaging Scientist Award and a Humboldt Prize and the coauthor, with William Swindell, of Radiological Imaging: The Theory of Image Formation, Detection, and Processing.
KYLE J. MYERS received a BS in Mathematics and Physics from Occidental College and an MS and PhD in Optical Sciences from the University of Arizona. Dr. Myers is the Chief of the Medical Imaging and Computer Applications Branch of the Center for Devices and Radiological Health of the U.S. Food and Drug Administration. She is a member of the SPIE, the Optical Society of America, and the Medical Image Perception Society (MIPS), and recently served as cochair of the Medical Image Perception Conference sponsored by MIPS.

"...an impressive tour-de-force textbook of imaging systems that deserves a place on the bookshelves of many radiologists and students." ( Yale Journal of Biology and Medicine , July 2005)
"...a worthwhile addition to the armamentarium of any serious researcher in image science and will be an opt-quoted reference for many years to come." ( Journal of Electrical Imaging , April-June 2005)

In an article whether educational programs for imaging physicists should emphasize science of imaging rather than the technology of imaging, "The new textbook...does appear to be outstanding. It contains over 1500 pages of text, with probably about as many equations..." ( Medical Physics , October 2004)

" Foundation of Image Science is comprehensive and the mathematics is rigorous and ubiquitous." ( E-Streams , Vol. 7, No. 5)

"Containing a clear, detailed and general mathematical description of image formation, representation, and quality assessment, this book will be of great interest to researches and graduate students...highly recommended." ( Medical Physics )