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Nonlinear Signal Processing：A Statistical Approach.pdf

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    Nonlinear Signal Processing: A Statistical Approach
    Preface
    Acknowledgments
    Contents
    Acronyms
    1 Introduction
    1.1 NonGaussian Random Processes
    1.1.1 Generalized Gaussian Distributions and Weighted Medians
    1.1.2 Stable Distributions and Weighted Myriads
    1.2 Statistical Foundations
    1.3 The Filtering Problem
    1.3.1 Moment Theory
    2 NonGaussian Models
    2.1 Generalized Gaussian Distributions
    2.2 Stable Distributions
    2.2.1 Definitions
    2.2.2 Symmetric Stable Distributions
    2.2.3 Generalized Central Limit Theorem
    2.2.4 Simulation of Stable Sequences
    2.3 Lower-Order Moments
    2.3.1 Fractional Lower-Order Moments
    2.3.2 Zero-Order Statistics
    2.3.3 Parameter Estimation of Stable Distributions
    Problems
    3 Order Statistics
    3.1 Distributions Of Order Statistics
    3.2 Moments Of Order Statistics
    3.2.1 Order Statistics From Uniform Distributions
    3.2.2 Recurrence Relations
    3.3 Order Statistics Containing Outliers
    3.4 Joint Statistics Of Ordered And NonOrdered Samples
    Problems
    4 Statistical Foundations of Filtering
    4.1 Properties of Estimators
    4.2 Maximum Likelihood Estimation
    4.3 Robust Estimation
    Problems
    5 Median and Weighted Median Smoothers
    5.1 Running Median Smoothers
    5.1.1 Statistical Properties
    5.1.2 Root Signals (Fixed Points)
    5.2 Weighted Median Smoothers
    5.2.1 The Center-Weighted Median Smoother
    5.2.2 Permutation-Weighted Median Smoothers
    5.3 Threshold Decomposition Representation
    5.3.1 Stack Smoothers
    5.4 Weighted Medians in Least Absolute Deviation (LAD) Regression
    5.4.1 Foundation and Cost Functions
    5.4.2 LAD Regression with Weighted Medians
    5.4.3 Simulation
    Problems
    6 Weighted Median Filters
    6.1 Weighted Median Filters With Real-Valued Weights
    6.1.1 Permutation-Weighted Median Filters
    6.2 Spectral Design of Weighted Median Filters
    6.2.1 Median Smoothers and Sample Selection Probabilities
    6.2.2 SSPs for Weighted Median Smoothers
    6.2.3 Synthesis of WM Smoothers
    6.2.4 General Iterative Solution
    6.2.5 Spectral Design of Weighted Median Filters Admitting Real-Valued Weights
    6.3 The Optimal Weighted Median Filtering Problem
    6.3.1 Threshold Decomposition For Real-Valued Signals
    6.3.2 The Least Mean Absolute (LMA) Algorithm
    6.4 Recursive Weighted Median Filters
    6.4.1 Threshold Decomposition Representation of Recursive WM Filters
    6.4.2 Optimal Recursive Weighted Median Filtering
    6.5 Mirrored Threshold Decomposition and Stack Filters
    6.5.1 Stack Filters
    6.5.2 Stack Filter Representation of Recursive WM Filters
    6.6 Complex-Valued Weighted Median Filters
    6.6.1 Phase-Coupled Complex WM Filter
    6.6.2 Marginal Phase-Coupled Complex WM Filter
    6.6.3 Complex threshold decomposition
    6.6.4 Optimal Marginal Phase-Coupled Complex WM
    6.6.5 Spectral Design of Complex-Valued Weighted Medians
    6.7 Weighted Median Filters for Multichannel Signals
    6.7.1 Marginal WM filter
    6.7.2 Vector WM filter
    6.7.3 Weighted Multichannel Median Filtering Structures
    6.7.4 Filter Optimization
    Problems
    7 Linear Combination of Order Statistics
    7.1 L-Estimates of Location
    7.2 L-Smoothers
    7.3 Ll-Filters
    7.3.1 Design and Optimization of Ll filters
    7.4 Ljl Permutation Filters
    7.5 Hybrid Media/Linear FIR Filters
    7.5.1 Median and FIR Affinity Trimming
    7.6 Linear Combination of Weighted Medians
    7.6.1 LCWM Filters
    7.6.2 Design of LCWM filters
    7.6.3 Symmetric LCWM Filters
    Problems
    8 Myriad Smoothers
    8.1 FLOM Smoothers
    8.2 Running Myriad Smoothers
    8.3 Optimality of the Sample Myriad
    8.4 Weighted Myriad Smoothers
    8.5 Fast Weighted Myriad Computation
    8.6 Weighted Myriad Smoother Design
    8.6.1 Center-Weighted Myriads for Image Denoising
    8.6.2 Myriadization
    Problems
    9 Weighted Myriad Filters
    9.1 Weighted Myriad Filters With Real-Valued Weights
    9.2 Fast Real-valued Weighted Myriad Computation
    9.3 Weighted Myriad Filter Design
    9.3.1 Myriadization
    9.3.2 Optimization
    Problems
    References
    Appendix A Software Guide
    Index
    Nonlinear Signal Processing A Statistical Approach Gonzalo R. Arce University of Delaware Department of Computer and Electrical Engineering @ E E i C I E N C E A JOHN WILEY & SONS, INC., PUBLICATION
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    Nonlinear Signal Processing
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    Nonlinear Signal Processing A Statistical Approach Gonzalo R. Arce University of Delaware Department of Computer and Electrical Engineering @ E E i C I E N C E A JOHN WILEY & SONS, INC., PUBLICATION
    Copyright 0 2005 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 11 1 River Street, Hoboken, NJ 07030, (201) 748-601 1, fax (201) 748-6008. Limit of LiabilityiDisclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representation or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services please contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993 or fax 317-572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print, however, may not be available in electronic format. Library of Congress Cataloging-in-Publication Data: Nonlinear signal processing : a statistical approach / Gonzalo R. Arce Includes bibliographical references and index. ISBN 0-471-67624-1 (cloth : acid-free paper) 1. Signal processing-Mathematics. 2. Statistics. I. Title. 2004042240 Arce, Gonzalo R. p. cm. TK5102.9.A77 2004 6 2 1 . 3 8 2 ' 2 4 ~ 2 2 Printed in the United States of America 1 0 9 8 7 6 5 4 3 2 1
    To Catherine, Andrew, Catie, and my beloved parents.
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