Random processes for image and signal processing / Edward R. Dougherty.

Format:

Book

Author/Creator:

Dougherty, Edward R.

Contributor:

Society of Photo-Optical Instrumentation Engineers.

Series:

SPIE/IEEE series on imaging science & engineering.

SPI/IEEE series on imaging science & engineering

Language:

English

Subjects (All):

Image processing--Statistical methods.

Image processing.

Stochastic processes.

Signal processing--Statistical methods.

Signal processing.

Physical Description:

1 online resource (611 p.)

Place of Publication:

Bellingham, Wash. : SPIE Optical Engineering Press ; New York : Institute of Electrical and Electronics Engineers, c1999.

Language Note:

English

Summary:

Part of the SPIE/IEEE Series on Imaging Science and Engineering. This book provides a framework for understanding the ensemble of temporal, spatial, and higher-dimensional processes in science and engineering that vary randomly in observations. Suitable as a text for undergraduate and graduate students with a strong background in probability and as a graduate text in image processing courses.

Contents:

Chapter 1. Probability theory

Probability space

Events

Conditional probability

Random variables

Probability distributions

Probability densities

Functions of a random variable

Moments

Expectation and variance

Moment-generating function

Important probability distributions

Binomial distribution

Poisson distribution

Normal distribution

Gamma distribution

Beta distribution

Computer simulation

Multivariate distributions

Jointly distributed random variables

Conditioning

Independence

Functions of several random variables

Basic arithmetic functions of two random variables

Distributions of sums of independent random variables

Joint distributions of output random variables

Expectation of a function of several random variables

Covariance

Multivariate normal distribution

Laws of large numbers

Weak law of large numbers

Strong law of large numbers

Central limit theorem

Parametric estimation via random samples

Random-sample estimators

Sample mean and sample variance

Minimum-variance unbiased estimators

Method of moments

Order statistics

Maximum-likelihood estimation

Maximum-likelihood estimators

Additive noise

Minimum noise

Entropy

Uncertainty

Information

Entropy of a random vector

Source coding

Prefix codes

Optimal coding

Exercises for chapter 1.

Chapter 2. Random processes

Random functions

Moments of a random function

Mean and covariance functions

Mean and covariance of a sum

Differentiation

Differentiation of random functions

Mean-square differentiability

Integration

Mean ergodicity

Poisson process

One-dimensional Poisson model

Derivative of the Poisson process

Properties of Poisson points

Axiomatic formulation of the Poisson process

Wiener process and white noise

White noise

Random walk

Wiener process

Stationarity

Wide-sense stationarity

Mean-ergodicity for WS stationary processes

Covariance-ergodicity for WS stationary processes

Strict-sense stationarity

Estimation

Linear systems

Communication of a linear operator with expectation

Representation of linear operators

Output covariance

Exercises for chapter 2.

Chapter 3. Canonical representation

Canonical expansions

Fourier representation and projections

Expansion of the covariance function

Karhunen-Loeve expansion

The Karhunen-Loeve theorem

Discrete Karhunen-Loeve expansion

Canonical expansions with orthonormal coordinate functions

Relation to data compression

Noncanonical representation

Generalized Bessel inequality

Decorrelation

Trigonometric representation

Trigonometric Fourier series

Generalized Fourier coefficients for WS stationary processes

Mean-square periodic WS stationary processes

Expansions as transforms

Orthonormal transforms of random functions

Fourier descriptors

Transform coding

Karhunen-Loeve compression

Transform compression using arbitrary orthonormal systems

Walsh-Hadamard transform

Discrete cosine transform

Transform coding for digital images

Optimality of the Karhunen-Loeve transform

Coefficients generated by linear functionals

Coefficients from integral functionals

Generating bi-orthogonal function systems

Complete function systems

Canonical expansion of the covariance function

Canonical expansions from covariance expansions

Constructing canonical expansions for covariance functions

Integral canonical expansions

Construction via integral functional coefficients

Construction from a covariance expansion

Power spectral density

The power-spectral-density/autocorrelation transform pair

Power spectral density and linear operators

Integral representation of WS stationary random functions

Canonical representation of vector random functions

Vector random functions

Canonical expansions for vector random functions

Finite sets of random vectors

Canonical representation over a discrete set

Exercises for chapter 3.

Chapter 4. Optimal filtering

Optimal mean-square-error filters

Conditional expectation

Optimal nonlinear filter

Optimal filter for jointly normal random variables

Multiple observation variables

Bayesian parametric estimation

Optimal finite-observation linear filters

Linear filters and the orthogonality principle

Design of the optimal linear filter

Optimal linear filter in the jointly Gaussian case

Role of wide-sense stationarity

Signal-plus-noise model

Edge detection

Steepest descent

Steepest descent iterative algorithm

Convergence of the steepest-descent algorithm

Least-mean-square adaptive algorithm

Convergence of the LMS algorithm

Nonstationary processes

Least-squares estimation

Pseudoinverse estimator

Least-squares estimation for nonwhite noise

Multiple linear regression

Least-squares image restoration

Optimal linear estimation of random vectors

Optimal linear filter for linearly dependent observations

Optimal estimation of random vectors

Optimal linear filters for random vectors

Recursive linear filters

Recursive generation of direct sums

Static recursive optimal linear filtering

Dynamic recursive optimal linear filtering

Optimal infinite-observation linear filters

Wiener-Hopf equation

Wiener filter

Optimal linear filter in the context of a linear model

The linear signal model

Procedure for finding the optimal linear filter

Additive white noise

Discrete domains

Optimal linear filters via canonical expansions

Integral decomposition into white noise

Integral equations involving the autocorrelation function

Solution via discrete canonical expansions

Optimal binary filters

Binary conditional expectation

Boolean functions and optimal translation-invariant filters

Optimal increasing filters

Pattern classification

Optimal classifiers

Gaussian maximum-likelihood classification

Linear discriminants

Neural networks

Two-layer neural networks

Steepest descent for nonquadratic error surfaces

Sum-of-squares error

Error back-propagation

Error back-propagation for multiple outputs

Adaptive network design

Exercises for chapter 4.

Chapter 5. Random models

Markov chains

Chapman-Kolmogorov equations

Transition probability matrix

Markov processes

Steady-state distributions for discrete-time Markov chains

Long-run behavior of a two-state Markov chain

Classification of states

Steady-state and stationary distributions

Long-run behavior of finite Markov chains

Long-run behavior of Markov chains with infinite state spaces

Steady-state distributions for continuous-time Markov chains

Irreducible continuous-time Markov chains

Birth-death model-queues

Forward and backward Kolmogorov equations

Markov random fields

Neighborhood systems

Determination by conditional probabilities

Gibbs distributions

Random Boolean model

Germ-grain model

Vacancy

Hitting

Linear boolean model

Granulometries

Openings

Classification by granulometric moments

Adaptive reconstructive openings

Random sets

Hit-or-miss topology

Convergence and continuity

Random closed sets

Capacity functional

Exercises for chapter 5

Bibliography

Index.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9781615837359

1615837353

9780819478450

0819478458

OCLC:

631155257