1st Edition

Nonlinear Signal and Image Processing Theory, Methods, and Applications

Edited By Kenneth E. Barner, Gonzalo R. Arce Copyright 2003
    560 Pages 472 B/W Illustrations
    by CRC Press

    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.

    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

    Biography

    Kenneth E. Barner, Gonzalo R. Arce