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Informationen zum Autor 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. Klappentext A comprehensive treatment of the principles, mathematics, and statistics of image science In today's visually oriented society, images play an important role in conveying messages. From seismic imaging to satellite images to medical images, our modern society would be lost without images to enhance our understanding of our health, our culture, and our world. Foundations of Image Science presents a comprehensive treatment of the principles, mathematics, and statistics needed to understand and evaluate imaging systems. The book is the first to provide a thorough treatment of the continuous-to-discrete, or CD, model of digital imaging. Foundations of Image Science emphasizes the need for meaningful, objective assessment of image quality and presents the necessary tools for this purpose. Approaching the subject within a well-defined theoretical and physical context, this landmark text presents the mathematical underpinnings of image science at a level that is accessible to graduate students and practitioners working with imaging systems, as well as well-motivated undergraduate students. Destined to become a standard text in the field, Foundations of Image Science covers: Mathematical Foundations: Examines the essential mathematical foundations of image science Image Formation-Models and Mechanisms: Presents a comprehensive and unified treatment of the mathematical and statistical principles of imaging, with an emphasis on digital imaging systems and the use of SVD methods Image Quality: Provides a systematic exposition of the methodology for objective or task-based assessment of image quality Applications: Presents detailed case studies of specific direct and indirect imaging systems and provides examples of how to apply the various mathematical tools covered in the book Appendices: Covers the prerequisite material necessary for understanding the material in the main text, including matrix algebra, complex variables, and the basics of probability theory Zusammenfassung In a visually oriented computer dominated society, images play an important role in conveying messages. This book presents a coherent treatment of the principles, mathematics, and statistics needed to understand imaging systems. The diverse imaging systems are treated within a theoretical and experimental context. Inhaltsverzeichnis 1. VECTORS AND OPERATORS. 1.1 LINEAR VECTOR SPACES. 1.1.1 Vector addition and scalar multiplication. 1.1.2 Metric spaces and norms. 1.1.3 Sequences of vectors and complete metric spaces. 1.1.4 Scalar products and Hilbert space. 1.1.5 Basis vectors. 1.1.6 Continuous bases. 1.2 TYPES OF OPERATORS. 1.2.1 Functions and functionals. 1....
List of contents
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 PROCESSES.
8.4 STOCHASTIC MODELS FOR OBJECTS.
8.5 STOCHASTIC MODELS FOR IMAGES.
9. DIFFRACTION THEORY AND IMAGING.
9.1 WAVE EQUATIONS.
9.2 PLANE WAVES AND SPHERICAL WAVES.
9.3 GREEN'S FUNCTIONS.
9.4 DIFFRACTION BY A PLANAR APERTURE.
9.5 DIFFRACTION IN THE FREQUENCY DOMAIN.
9.6 IMAGING OF POINT OBJECTS.
9.7 IMAGING OF EXTENDED PLANAR OBJECTS.
9.8 VOLUME DIFFRACTION AND 3D IMAGING.
10. ENERGY TRANSPORT AND PHOTONS.
10.1 ELECTROMAGNETIC ENERGY FLOW AND DETECTION.
10.2 RADIOMETRIC QUANTITIES AND UNITS.
10.3 THE BOLTZMANN TRANSPORT EQUATION.
10.4 TRANSPORT THEORY AND IMAGING.
11. POISSON STATISTICS AND PHOTON COUNTING.
11.1 POISSON RANDOM VARIABLES.
11.2 POISSON RANDOM VECTORS.
11.3 RANDOM POINT PROCESSES.
11.4 RANDOM AMPLIFICATION.
11.5 QUANTUM MECHANICS OF PHOTON COUNTING.
12. NOISE IN DETECTORS.
12.1 PHOTON NOISE AND SHOT NOISE IN PHOTODIODES.
12.2 OTHER NOISE MECHANISMS.
12.3 X-RAY AND GAMMA-RAY DETECTORS.
13. STATISTICAL DECISION THEORY.
13.1 BASIC CONCEPTS.
13.2 CLASSIFICATION TASKS.
13.3 ESTIMATION THEORY.
14. IMAGE QUALITY.
14.1 SURVEY OF APPROACHES.
14.2 HUMAN OBSERVERS AND CLASSIFICATION TASKS.
14.3 MODEL OBSERVERS AND CLASSIFICATION TASKS.
14.4 ESTIMATION TASKS.
14.5 SOURCES OF IMAGES.
15. INVERSE PROBLEMS.
15.1 BASIC CONCEPTS.
15.2 LINEAR RECONSTRUCTION OPERATORS.
15.3 IMP
Report
"...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 )
