Foundations of Image Science

ISBN-10: 0471153001

ISBN-13: 9780471153009

Edition: 2004

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Description: This text presents the fundamental physics at work in imaging systems. It offers a coherent treatment of the principles, mathematics and statistics needed to understand imaging systems.

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Book details

List price: $253.00
Copyright year: 2004
Publisher: John Wiley & Sons, Incorporated
Publication date: 10/24/2003
Binding: Hardcover
Pages: 1584
Size: 10.25" wide x 7.75" long x 2.25" tall
Weight: 6.424
Language: English

Vectors and Operators
Linear Vector Spaces
Vector addition and scalar multiplication
Metric spaces and norms
Sequences of vectors and complete metric spaces
Scalar products and Hilbert space
Basis vectors
Continuous bases
Types of Operators
Functions and functionals
Integral transforms
Matrix operators
Continuous-to-discrete mappings
Differential operators
Hilbert-Space Operators
Range and domain
Linearity, boundedness and continuity
Inverse operators
Adjoint operators
Projection operators
Outer products
Eigenvectors and eigenvalue spectra
Similarity transformations
Eigenanalysis in finite-dimensional spaces
Eigenanalysis of Hermitian operators
Diagonalization of a Hermitian operator
Simultaneous diagonalization of Hermitian matrices
Singular-Value Decomposition
Definition and properties
SVD representations of vectors and operators
Moore-Penrose Pseudoinverse
Penrose equations
Pseudoinverses and SVD
Properties of the pseudoinverse
Pseudoinverses and projection operators
Pseudoinverses and Linear Equations
Nature of solutions of linear equations
Existence and uniqueness of exact solutions
Explicit solutions for consistent data
Least-squares solutions
Minimum-norm solutions
Iterative calculation of pseudoinverse solutions
Reproducing-Kernel Hilbert Space
Positive-definite Hermitian operators
Nonnegative-definite Hermitian operators
The Dirac Delta and Other Generalized Functions
Theory of Distributions
Basic concepts
Well-behaved functions
Approximation of other functions
Formal definition of distributions
Properties of distributions
Tempered distributions
One-Dimensional Delta Function
Intuitive definition and elementary properties
Limiting representations
Distributional approach
Derivatives of delta functions
A synthesis
Delta functions as basis vectors
Other Generalized Functions in 1D
Generalized functions as limits
Generalized functions related to the delta function
Other point singularities
Multidimensional Delta Functions
Multidimensional distributions
Multidimensional delta functions
Delta functions in polar coordinates
Line masses and plane masses
Multidimensional derivatives of delta functions
Other point singularities
Angular delta functions
Fourier Analysis
Sines, Cosines and Complex Exponentials
Orthogonality on a finite interval
Complex exponentials
Orthogonality on the infinite interval
Discrete orthogonality
View from the complex plane
Fourier Series
Basic concepts
Convergence of the Fourier series
Properties of the Fourier coefficients
1D Fourier Transform
Basic concepts
Convergence issues
Unitarity of the Fourier operator
Fourier transforms of generalized functions
Properties of the 1D Fourier transform
Convolution and correlation
Fourier transforms of some special functions
Relation between Fourier series and Fourier transforms
Analyticity of Fourier transforms
Related transforms
Multidimensional Fourier Transforms
Basis functions
Definitions and elementary properties
Multidimensional convolution and correlation
Rotationally symmetric functions
Some special functions and their transforms
Multidimensional periodicity
Sampling Theory
Bandlimited functions
Reconstruction of a bandlimited function from uniform samples
Sampling in frequency space
Multidimensional sampling
Sampling with a finite aperture
Discrete Fourier Transform
Motivation and definitions
Basic properties of the DFT
Relation between discrete and continuous Fourier transforms
Discrete-Space Fourier Transform
Fast Fourier Transform
Multidimensional DFTs
Series Expansions and Integral Transforms
Expansions in Orthogonal Functions
Basic concepts
Orthogonal polynomials
Sturm-Liouville theory
Classical orthogonal polynomials and related functions
Prolate spheroidal wavefunctions
Classical Integral Transforms
Laplace transform
Mellin transform
z transform
Hilbert transform
Higher-order Hankel transforms
Fresnel Integrals and Transforms
Fresnel integrals
Fresnel transforms
Chirps and Fourier transforms
Radon Transform
2D Radon transform and its adjoint
Central-slice theorem
Filtered backprojection
Unfiltered backprojection
Radon transform in higher dimensions
Radon transform in signal processing
Mixed Representations
Local Spectral Analysis
Local Fourier transforms
Local frequency
Gabor's signal expansion
Bilinear Transforms
Wigner distribution function
Ambiguity functions
Fractional Fourier transforms
Mother wavelets and scaling functions
Continuous wavelet transform
Discrete wavelet transform
Multiresolution analysis
Group Theory
Basic Concepts
Definition of a group
Group multiplication tables
Isomorphism and homomorphism
Subgroups and Classes
Group Representations
Matrices that obey the multiplication table
Irreducible representations
Unitary irreducible representations and orthogonality properties
Some Finite Groups
Cyclic groups
Dihedral groups
Continuous Groups
Basic properties
Linear, orthogonal and unitary groups
Abelian and non-Abelian Lie groups
Groups of Operators on a Hilbert Space
Geometrical transformations of functions
Invariant subspaces
Irreducible subspaces
Orthogonality of basis functions
Quantum Mechanics and Image Science
Smattering of quantum mechanics
Connection with image science
Symmetry group of the Hamiltonian
Symmetry and degeneracy
Reducibility and accidental degeneracy
Rotational symmetry in three dimensions
Functions and Transforms on Groups
Functions on a finite group
Extension to infinite groups
Convolutions on groups
Fourier transforms on groups
Wavelets revisited
Deterministic Descriptions of Imaging Systems
Objects and Images
Objects and images as functions
Objects and images as infinite-dimensional vectors
Objects and images as finite-dimensional vectors
Representation accuracy
Uniform translates
Other representations
Linear Continuous-To-Continuous Systems
General shift-variant systems
Adjoint operators and SVD
Shift-invariant systems
Eigenanalysis of LSIV systems
Singular-value decomposition of LSIV systems
Transfer functions
Approximately shift-invariant systems
Rotationally symmetric systems
Axial systems
Linear Continuous-to-Discrete Systems
System operator
Adjoint operator and singular-value decomposition
Fourier description
Sampled LSIV systems
Mixed CC-CD systems
Discrete-to-continuous systems
Linear Discrete-to-Discrete Systems
System matrix
Adjoint operator and singular-value decomposition
Image errors
Discrete representations of shift-invariant systems
Nonlinear Systems
Point nonlinearities
Nonlocal nonlinearities
Object-dependent system operators
Postdetection nonlinear operations
Stochastic Descriptions of Objects and Images
Random Vectors
Basic concepts
Covariance and correlation matrices
Characteristic functions
Transformations of random vectors
Eigenanalysis of covariance matrices
Random Processes
Definitions and basic concepts
Averages of random processes
Characteristic functionals
Correlation analysis
Spectral analysis
Linear filtering of random processes
Eigenanalysis of the autocorrelation operator
Discrete random processes
Normal Random Vectors and Processes
Probability density functions
Characteristic function
Marginal densities and linear transformations
Central-limit theorem
Normal random processes
Complex Gaussian random fields
Stochastic Models for Objects
Probability density functions in Hilbert space
Multipoint densities
Normal models
Texture models
Signals and backgrounds
Stochastic Models for Images
Linear systems
Conditional statistics for a single object
Effects of object randomness
Signals and backgrounds in image space
Diffraction Theory and Imaging
Wave Equations
Maxwell's equations
Maxwell's equations in the Fourier domain
Material media
Time-dependent wave equations
Time-independent wave equations
Plane Waves and Spherical Waves
Plane waves
Spherical waves
Green's Functions
Differential equations for the Green's functions
Time-dependent Green's function
Green's functions for the Helmholtz and Poisson equations
Defined-source problems
Boundary-value problems
Diffraction by a Planar Aperture
Surface at infinity
Kirchhoff boundary conditions
Application of Green's theorem
Diffraction as a 2D linear filter
Some useful approximations
Fresnel diffraction
Fraunhofer diffraction
Diffraction in the Frequency Domain
Angular spectrum
Fresnel and Fraunhofer approximations
Reflection and refraction of light
Imaging of Point Objects
Ideal thin lens
Imaging a monochromatic point source
Transmittance of an aberrated lens
Rotationally symmetric lenses
Field curvature and distortion
Probing the pupil
Interpretation of the other Seidel aberrations
Imaging of Extended Planar Objects
Monochromatic objects and a simple lens
4f imaging system
More complicated lens systems
Random fields and coherence
Quasimonochromatic imaging
Spatially incoherent, quasimonochromatic imaging
Polychromatic, incoherent imaging
Partially coherent imaging
Volume Diffraction and 3D Imaging
Born approximation
Rytov approximation
Fraunhofer diffraction from volume objects
Coherent 3D imaging
Energy Transport and Photons
Electromagnetic Energy Flow and Detection
Energy flow in classical electrodynamics
Plane waves
Physics of photodetection
What do real detectors detect?
Radiometric Quantities and Units
Self-luminous surface objects
Self-luminous volume objects
Surface reflection and scattering
Transmissive objects
Cross sections
Distribution function
Radiance in physical optics and quantum optics
Boltzmann Transport Equation
Derivation of the Boltzmann equation
Steady-state solutions in non-absorbing media
Steady-state solutions in absorbing media
Scattering effects
Spherical harmonics
Elastic scattering and diffusion
Inelastic (Compton) scattering
Transport Theory and Imaging
General imaging equation
Pinhole imaging
Optical imaging of a planar source
Adjoint methods
Monte Carlo methods
Poisson Statistics and Photon Counting
Poisson Random Variables
Poisson and independence
Poisson and rarity
Binomial selection of a Poisson
Doubly stochastic Poisson random variables
Poisson Random Vectors
Multivariate Poisson statistics
Doubly stochastic multivariate statistics
Random Point Processes
Temporal point processes
Spatial point processes
Mean and autocorrelation of point processes
Relation between Poisson random vectors and processes
Karhunen-Loeve analysis of Poisson processes
Doubly stochastic spatial Poisson random processes
Doubly stochastic temporal Poisson random processes
Point processes in other domains
Filtered point processes
Characteristic functionals of filtered point processes
Spectral properties of point processes
Random Amplification
Random amplification in single-element detectors
Random amplification and generating functions
Random amplification of point processes
Spectral analysis
Random amplification in arrays
Quantum Mechanics of Photon Counting
Coherent states
Density operators
Counting statistics
Noise in Detectors
Photon Noise and Shot Noise in Photodiodes
Vacuum photodiodes
Basics of semiconductor detectors
Shot noise in semiconductor photodiodes
Other Noise Mechanisms
Thermal noise
Generation-recombination noise
1 / f noise
Noise in gated integrators
Arrays of noisy photodetectors
X-ray and Gamma-Ray Detectors
Interaction mechanisms
Photon-counting semiconductor detectors
Semiconductor detector arrays
Position and energy estimation with semiconductor detectors
Scintillation cameras
Position and energy estimation with scintillation cameras
Imaging characteristics of photon-counting detectors
Integrating detectors
K x rays and Compton scattering
Statistical Decision Theory
Basic Concepts
Kinds of decisions
Inputs to the process
Classification Tasks
Partitioning the data space
Binary decision outcomes
The ROC curve
Performance measures for binary tasks
Computation of AUC
The likelihood ratio and the ideal observer
Statistical properties of the likelihood ratio
Ideal observer with Gaussian statistics
Ideal observer with non-Gaussian data
Signal variability and the ideal observer
Background variability and the ideal observer
The optimal linear discriminant
Detectability in continuous data
Estimation Theory
Basic concepts
MSE in digital imaging
Bayesian estimation
Maximum-likelihood estimation
Likelihood and Fisher information
Properties of ML estimators
Other classical estimators
Nuisance parameters
Hybrid detection / estimation tasks
Image Quality
Survey of Approaches
Subjective assessment
Fidelity measures
JND models
Information-theoretic assessment
Objective assessment of image quality
Human Observers and Classification Tasks
Methods for investigating the visual system
Modified ideal-observer models
Psychophysical methods for image evaluation
Estimation of figures of merit
Model Observers
General considerations
Linear observers
Ideal observers
Estimation tasks
Sources of Images
Deterministic simulation of objects
Stochastic simulation of objects
Deterministic simulation of image formation
Stochastic simulation of image formation
Gold standards
Inverse Problems
Basic Concepts
Classifications of inverse problems
Discretization dilemma
Choosing the best algorithm
Linear Reconstruction Operators
Matrix operators for estimation of expansion coefficients
Reconstruction of functions from discrete data
Reconstruction from Fourier samples
Discretization of analytic inverses
More on analytic inverses
Noise with linear reconstruction operators
Implicit Estimates
Functional minimization
Data-agreement functionals
Regularizing functionals
Effects of positivity
Reconstruction without discretization
Resolution and noise in implicit estimates
Iterative Algorithms
Linear iterative algorithms
Noise propagation in linear algorithms
Search algorithms for functional minimization
Nonlinear constraints and fixed-point iterations
Projections onto convex sets
MLEM algorithm
Noise propagation in nonlinear algorithms
Stochastic algorithms
Planar Imaging With X Rays and Gamma Rays
Digital Radiography
The source and the object
X-ray detection
Scattered radiation
Deterministic properties of shadow images
Stochastic properties
Image quality: Detection tasks
Image quality: Estimation tasks
Planar Imaging in Nuclear Medicine
Basic issues
Image formation
The detector
Stochastic properties
Image quality: Classification tasks
Image quality: Estimation tasks
Emission Computed Tomography
Forward Problems
CD formulations for parallel-beam SPECT
Equally spaced angles
Fourier analysis in the CD formulation
2D Radon transform and parallel-beam SPECT
3D transforms and cone-beam SPECT
Inverse Problems
SVD of the 2D Radon transform
Inverses and pseudoinverses in 2D
Inversion of the 3D x-ray transform
Inversion of attenuated transforms
Discretization of analytic reconstruction algorithms
Matrices for iterative methods
Noise and Image Quality
Noise in the data
Noise in reconstructed images
Image quality
Basic Concepts
Elementary statistical considerations
Speckle in imaging
Speckle in a Nonimaging System
Description of the ground glass
Some simplifying assumptions
Propagation of characteristic functionals
Central-limit theorem
Statistics of the irradiance
Speckle in an Imaging System
The imaging system
Propagation of characteristic functionals
Effect of the detector
Noise and Image Quality
Measurement noise
Random objects
Task performance
Point-Scattering Models and Non-Gaussian Speckle
Object fields and objects
Image fields
Univariate statistics of the image field and irradiance
Coherent Ranging
System configurations
Deterministic analysis
Statistical analysis
Task performance
Imaging in Fourier Space
Fourier Modulators
Data acquisition
Image quality
Young's double-slit experiment
Visibility estimation
Michelson stellar interferometer
Interferometers with multiple telescopes
Epilogue: Frontiers in Image Science
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