Science Book from C.H.I.P.S.

Foundations of Image Science
by Harrison H. Barrett
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 continuoustodiscrete, or CD, model of digital imaging.
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 taskbased 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
Contents
1. Vectors and Operators
 Linear Vector Spaces
 Types of Operators
 HilbertSpace Operators
 Eigenanalysis
 SingularValue Decomposition
 MoorePenrose Pseudoinverse
 Pseudoinverses and Linear Equations
 ReproducingKernel Hilbert Space
2. The Dirac Delta and Other Generalized Functions
 Theory of Distributions
 OneDimensional Delta Function
 Other Generalized Functions in 1D
 Multidimensional Delta Functions
3. Fourier Analysis
 Sines, Cosines and Complex Exponentials
 Fourier Series
 1D Fourier Transform
 Multidimensional Fourier Tranforms
 Sampling Theory
 Discrete Fourier Transform
4. Series Expansions and Integral Tranforms
 Expansions in Orthogonal Functions
 Classical Integral Transforms
 Fresnel Integrals and Transforms
 Radon Transform
5. Mixed Representations
 Local Spectral Analysis
 Bilinear Transforms
 Wavelets
6. Group Therapy
 Basic Concepts
 Subgroups and Classes
 Group Representations
 Some Finite Groups
 Continious Groups
 Groups of Operators on a Hilbert Space
 Quatum Mechanics and Image Science
 Functions and Transforms on Groups
7. Deterministic Descriptions of Imaging Systems
 Objects and Images
 Linear ContinuoustoContinuous Systems
 Linear ContinuoustoDiscrete Systems
 Linear DiscretetoDiscrete Systems
 Nonlinear Systems
8. Stochastic Descriptions of Objects and Images
 Random Vectors
 Random Processes
 Normal Random Vectors and Processes
 Stochastic Models for Objects
 Stochastic Models for Images
9. Difraction Theory and Imaging
 Wave Equations
 Plane Waves and Spherical Waves
 Green's Functions
 Difraction by a Planar Aperture
 Difraction in the Frequency Domain
 Imaging of Point Objects
 Imaging of Extended Planar Objects
 Volume Difraction and 3D Imaging
10. Energy Transport and Photons
 Electromagnetic Energy Flow and Detection
 Radiometric Quatities and Units
 Boltzmann Transport Equation
 Transport Theory and Imaging
11. Poisson Statistics and Photon Counting
 Poisson Random Variables
 Poisson Random Vectors
 Random Point Processes
 Random Amplification
 Quantum Mechanics of Photon Counting
12. Noise in Detectors
 Photon Noise and Shot Noise in Photodiodes
 Other Noise Mechanisms
 XRay and GammaRay Detectors
13. Statistical Decision Theory
 Basic Concepts
 Classification Tasks
 Estimation Theory
14. Image Quality
 Survey of Approaches
 Human Observers and Classification Tasks
 Model Observers
 Sources of Images
15. Inverse Problems
 Basic Concepts
 Linear Reconstruction Operators
 Implicit Estimates
 Iterative Algorithms
16. Planar Imaging with X Rays and Gamma Rays
 Digital Radiography
 Planar Imaging in Nuclear Medicine
17. SinglePhoton Emission Computed Tomography
 Forward Problems
 Inverse Problems
 Noise and Image Quality
18. Coherent Imaging And Speckle
 Basic Concepts
 Speckle in a Nonimaging System
 Speckle in an Imaging System
 Noise and Image Quality
 PointScattering Models and NonGaussian Speckle
 Coherent Ranging
19. Imaging in Fourier Space
 Fourier Modulators
 Interferometers
Appendices
Index
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Foundations of Image Science
by Harrison H. Barrett
1,540 pages • $181.95 + shipping
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