Nonlinear signal and image processing methods are fast emerging as an alternative to established linear methods for meeting the challenges of increasingly sophisticated applications. Advances in computing performance and nonlinear theory are making nonlinear techniques not only viable, but practical.

This book details recent advances in nonlinear theory and methods and explores an array of modern signal and image processing applications. The first several chapters focus on nonlinear signal processing theory, targeting three critical areas: filter analysis, nonlinear filter class design, and signal analysis. The remaining chapters explore nonlinear approaches across the broad spectrum of applications with signal processing components, from data traffic modeling and image enhancement to cutting edge applications in genomics.

All of the chapters were contributed by well-known theorists and application-driven researchers who explore current and emerging nonlinear methods from their theoretical background and practical algorithms through the potential of these methods for solving important open questions. Nonlinear Signal and Image Processing: Theory, Methods, and Applications thus provides a singular opportunity to build a strong, fundamental understanding of nonlinear theory and methods and a foundation upon which to approach many of today's most interesting and challenging signal processing problems.

Table of Contents:
ENERGY CONSERVATION IN ADAPTIVE FILTERING
The Data Model
Energy-Conservation Relation
Weighted Variance Relation
Mean-Square Behavior
Mean-Square Stability
Steady-State Performance
Small Step-Size Approximation
Applications to Selected Filters
Fourth-Order Moment Approximation
Long Filter Approximation
Adaptive Filters with Error Nonlinearities
An Interpretation of the Energy Relation
Concluding Remarks
FUZZY METHODS IN NONLINEAR SIGNAL PROCESSING: PART I - THEORY
Maximum Likelihood Estimation and Spatial--Rank Ordering
Sample Affinity and Fuzzy Spatial--Rank Ordering
Fuzzy Filter Definition
Extensions to Multivariate Data
Conclusion
FUZZY METHODS IN NONLINEAR SIGNAL PROCESSING: PART II - APPLICATIONS
Introduction
Affine Filter Applications
Fuzzy Ordering and Fuzzy Median Filter Applications
Conclusions
TIME-FREQUENCY WIGNER DISTRIBUTION APPROACH TO DIFFERENTIAL EQUATIONS
Harmonic Oscillator with Chirp Driving Force
Approximation Method
Stochastic Processes
Partial Differential Equations
Conclusion
Acknowledgment
Appendix 1. Notations and definitions
APPENDIX 2. ORDINARY DIFFERENTIAL EQUATIONS
WEIGHTED MYRIAD FILTERS
Alpha-Stable Distributions
Running Myriad Smoothers
Optimality of the Sample Myriad in the Stable Model
Weighted Myriad Smoothers
Fast Weighted Myriad Computation
Weighted Myriad Smoother Design
Weighted Myriad Filters With Real-Valued Weights
Fast Real-valued Weighted Myriad Computation
Weighted Myriad Filter Design
DATA TRAFFIC MODELING - A SIGNAL PROCESSING PERSPECTIVE
Preliminaries-Self-similarity, Long-Range Dependence and Impulsiveness
The Self-similarity and Impulsive Nature of Data Traffic
Modeling Impulsive Self-Similar Data Traffic
Parameter Estimation
Concluding Remarks
NONLINEAR ADAPTIVE FILTERS FOR ACOUSTIC ECHO CANCELLATION IN MOBILE TERMINALS
Low-Complexity Nonlinear Adaptive Acoustic Echo Cancelers
Adaptive Algorithms for Nonlinear Acoustic Echo Cancelers
Experimental Results for Acoustic Echo Cancellation
Conclusions
BLIND AND SEMI-BLIND CHANNEL ESTIMATION
Introduction
Time-Varying Channel Model
Signal Properties Used in Blind Equalization
Receivers for MIMO Systems
Blind Receivers for Practical Wireless Systems
Blind Receivers for CDMA
Semi-Blind Techniques
Conclusion
BAYESIAN IMAGE AND VIDEO ENHANCEMENT USING A NON-GAUSSIAN PRIOR
Image and Video Observation Models
Regularization of Ill-Posed Inverse Problems
Simulations
Summary and Future Directions
STATISTICAL IMAGE MODELING AND PROCESSING USING WAVELET DOMAIN HIDDEN MARKOV MODELS
Wavelet-Domain Hidden Markov Models
Image Denoising
Image Segmentation
Conclusions
SELF-ORGANIZING MAPS AND THEIR APPLICATIONS IN IMAGE PROCESSING, INFORMATION ORGANIZATION, AND RETRIEVAL
Basic Feature-Mapping Models
Kohonen's Self-Organizing Map
Convergence Analysis of Self-Organizing Maps
Self-Organizing Map Properties
Variants of Self-Organizing Maps Based on Robust Statistics
A Class of Split-Merge Self-Organizing Maps
Conclusions
NONLINEAR TECHNIQUES FOR COLOR IMAGE PROCESSING
Adaptive Noise Reduction Filtering
Anisotropic Diffusion
Noise Reduction Filters for Color Image Processing
Digital Paths Approach to Color Image Filtering
Efficiency of the New Filter Class
GENETIC REGULATORY NETWORKS: A NONLINEAR SIGNAL PROCESSING PERSPECTIVE
Genetic Regulatory Networks
Boolean Networks
Concluding Remarks