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 continuous-to-discrete, 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 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


1. Vectors and Operators

  • Linear Vector Spaces
  • Types of Operators
  • Hilbert-Space Operators
  • Eigenanalysis
  • Singular-Value Decomposition
  • Moore-Penrose Pseudoinverse
  • Pseudoinverses and Linear Equations
  • Reproducing-Kernel Hilbert Space
2. The Dirac Delta and Other Generalized Functions

  • Theory of Distributions
  • One-Dimensional 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 Continuous-to-Continuous Systems
  • Linear Continuous-to-Discrete Systems
  • Linear Discrete-to-Discrete 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
  • X-Ray and Gamma-Ray 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. Single-Photon 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
  • Point-Scattering Models and Non-Gaussian Speckle
  • Coherent Ranging
19. Imaging in Fourier Space

  • Fourier Modulators
  • Interferometers



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Foundations of Image Science
by Harrison H. Barrett
1,540 pages • $181.95 + shipping
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