Foundations of Image Science
Wiley Series in Pure and Applied Optics
1. Edition November 2003
1584 Pages, Hardcover
Handbook/Reference Book
ISBN:
978-0-471-15300-9
John Wiley & Sons
Short Description
In today's visually oriented computer-dominated society, images play an important role in conveying messages. This will be the first book to present 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. This is not a how-to book describing the operation of imaging systems, but rather a thorough reference that presents the physics fundamentals behind imaging systems.
Presents the mathematical underpinnings of image science at an accessible level.
* The author is a preeminent researcher in the field and the past editor of the Journal of the Optical Society of America.
* This is the first book to present material with a well defined theoretical and experimental basis.
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 IMPLICIT ESTIMATES.
15.4 ITERATIVE ALGORITHMS.
16. PLANAR IMAGING WITH X RAYS AND GAMMA RAYS.
16.1 DIGITAL RADIOGRAPHY.
16.2 PLANAR NUCLEAR MEDICINE.
17. EMISSION COMPUTED TOMOGRAPHY.
17.1 FORWARD PROBLEMS.
17.2 INVERSE PROBLEMS.
17.3 NOISE AND IMAGE QUALITY.
18. SPECKLE.
18.1 BASIC CONCEPTS.
18.2 SPECKLE IN A NONIMAGING SYSTEMS.
18.3 SPECKLE IN AN IMAGING SYSTEM.
18.4 NOISE AND IMAGE QUALITY.
18.5 POINT-SCATTERINGMODELSANDNON-GAUSSIANSPECKLE.
18.6 COHERENT RANGING.
19. IMAGING IN FOURIER SPACE.
19.1 FOURIER MODULATORS.
19.2 INTERFEROMETERS.
EPILOGUE. FRONTIERS IN IMAGE SCIENCE.
A MATRIX ALGEBRA.
B COMPLEX VARIABLES.
C FUNDAMENTALS OF PROBABILITY.
Bibliography.
Index.
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 IMPLICIT ESTIMATES.
15.4 ITERATIVE ALGORITHMS.
16. PLANAR IMAGING WITH X RAYS AND GAMMA RAYS.
16.1 DIGITAL RADIOGRAPHY.
16.2 PLANAR NUCLEAR MEDICINE.
17. EMISSION COMPUTED TOMOGRAPHY.
17.1 FORWARD PROBLEMS.
17.2 INVERSE PROBLEMS.
17.3 NOISE AND IMAGE QUALITY.
18. SPECKLE.
18.1 BASIC CONCEPTS.
18.2 SPECKLE IN A NONIMAGING SYSTEMS.
18.3 SPECKLE IN AN IMAGING SYSTEM.
18.4 NOISE AND IMAGE QUALITY.
18.5 POINT-SCATTERINGMODELSANDNON-GAUSSIANSPECKLE.
18.6 COHERENT RANGING.
19. IMAGING IN FOURIER SPACE.
19.1 FOURIER MODULATORS.
19.2 INTERFEROMETERS.
EPILOGUE. FRONTIERS IN IMAGE SCIENCE.
A MATRIX ALGEBRA.
B COMPLEX VARIABLES.
C FUNDAMENTALS OF PROBABILITY.
Bibliography.
Index.
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.
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.
