Random Processes for Image and Signal Processing

Random Processes for Image and Signal Processing

Author(s): Edward R. Dougherty

Published: 1998

https://doi.org/10.1117/3.268105

PDF ISBN: 9780819478450 | Print ISBN: 9780819425133

DESCRIPTION

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.

Buy this book on SPIE.org

Buy this book on SPIE.org

Buy this book on SPIE.org

TABLE OF CONTENTS SHOW ALL CHAPTER OUTLINES +

SAVE THIS BOOK TO YOUR LIBRARY

Open Access

Front Matter

CHAPTER 1.

Probability Theory

Chapter Outline +

CHAPTER 2.

Random Processes

Chapter Outline +

CHAPTER 3.

Canonical Representation

Chapter Outline +

CHAPTER 4.

Optimal Filtering

Chapter Outline +

4.1. Optimal Mean-Square-Error Filters
4.1.1. Conditional Expectation
4.1.2. Optimal Nonlinear Filter
4.1.3. Optimal Filter for Jointly Normal Random Variables
4.1.4. Multiple Observation Variables
4.1.5. Bayesian Parametric Estimation
4.2. Optimal Finite-Observation Linear Filters
4.2.1. Linear Filters and the Orthogonality Principle
4.2.2. Design of the Optimal Linear Filter
4.2.3. Optimal Linear Filter in the Jointly Gaussian Case
4.2.4. Role of Wide-Sense Stationarity
4.2.5. Signal-plus-Noise Model
4.2.6. Edge Detection
4.3. Steepest Descent
4.3.1. Steepest Descent Iterative Algorithm
4.3.2. Convergence of the Steepest-Descent Algorithm
4.3.3. Least-Mean-Square Adaptive Algorithm
4.3.4. Convergence of the LMS Algorithm
4.3.5. Nonstationary Processes
4.4. Least-Squares Estimation
4.4.1. Pseudoinverse Estimator
4.4.2. Least-Squares Estimation for Nonwhite Noise
4.4.3. Multiple Linear Regression
4.4.4. Least-Squares Image Restoration
4.5. Optimal Linear Estimation of Random Vectors
4.5.1. Optimal Linear Filter for Linearly Dependent Observations
4.5.2. Optimal Estimation of Random Vectors
4.5.3. Optimal Linear Filters for Random Vectors
4.6. Recursive Linear Filters
4.6.1. Recursive Generation of Direct Sums
4.6.2. Static Recursive Optimal Linear Filtering
4.6.3. Dynamic Recursive Optimal Linear Filtering
4.7. Optimal Infinite-Observation Linear Filters
4.7.1. Wiener-Hopf Equation
4.7.2. Wiener Filter
4.8. Optimal Linear Filter in the Context of a Linear Model
4.8.1. The Linear Signal Model
4.8.2. Procedure for Finding the Optimal Linear Filter
4.8.3. Additive White Noise
4.8.4. Discrete Domains
4.9. Optimal Linear Filters via Canonical Expansions
4.9.1. Integral Decomposition into White Noise
4.9.2. Integral Equations Involving the Autocorrelation Function
4.9.3. Solution via Discrete Canonical Expansions
4.10. Optimal Binary Filters
4.10.1. Binary Conditional Expectation
4.10.2. Boolean Functions and Optimal Translation-Invariant Filters
4.10.3. Optimal Increasing Filters
4.11. Pattern Classification
4.11.1. Optimal Classifier
4.11.2. Gaussian Maximum-Likelihood Classification
4.11.3. Linear Discriminants
4.12. Neural Networks
4.12.1. Two-Layer Neural Networks
4.12.2. Steepest Descent for Nonquadratic Error Surfaces
4.12.3. Sum-of-Squares Error
4.12.4. Error Back-Propagation
4.12.5. Error Back-Propagation for Multiple Outputs
4.12.6. Adaptive Network Design
Exercises for Chapter 4

CHAPTER 5.

Random Models

Chapter Outline +

Open Access

Back Matter

Subscribe to Digital Library

Receive Email Alerts on Newly Released Titles

Buy this book on SPIE.org

Author a Spotlight

PUBLISH A SHORT TUTORIAL
OR OVERVIEW

Open Calls for Spotlights

Access & Subscriptions

SUBSCRIPTION AND MEMBERSHIP INFORMATION

Subscribe Today

Become an Author

JOIN THE DISTINGUISHED TEAM OF SPIE PRESS AUTHORS