Advances in Nonlinear Signal and Image Processing: Pt. 6(EURASIP Book Series on Signal Processing & Communications)

The interest in nonlinear methods in signal processing is steadily increasing, since nowadays the advances in computational capacities make it possible to implement sophisticated nonlinear processing techniques which in turn allow remarkable improvements with respect to standard and well-consolidated linear processing approaches. The aim of the book is to present a review of emerging new areas of interest involving nonlinear signal and image processing theories, techniques, and tools. More than 30 leading researchers have contributed to this book covering the major topics relevant to nonlinear signal processing. These topics include recent theoretical contributions in different areas of digital filtering and a number of applications in genomics, speech analysis and synthesis, communication system, active noise control, digital watermarking, feature extraction, texture analysis, and color image processing. The book is intended as a reference for recent advances and new applications of theories, techniques, and tools in the area of nonlinear signal processing. The target audience are graduate students and practitioners working on modern signal processing applications.

Table of Contents:
1. Nonstationary stochastic di.erential equations, Lorenzo Galleani and Leon Cohen 1 1.1. Introduction 1 1.2. Time-dependent power spectrum 2 1.3. The equation of motion for a nonstationary stochastic system 3 1.4. The nonstationaryWiener process 5 1.5. The Langevin equation: the full exact solution 7 1.6. Quantum Langevin equation 9 1.7. Time-variant random systems 10 1.8. Summary 13 Bibliography 13 2. Aperture filters: theory, application, and multiresolution analysis, Roberto Hirata Jr., Marcel Brun, Junior Barrera, and Edward R. Dougherty 15 2.1. Introduction 15 2.2. Window operators 17 2.3. Aperture operators 18 2.4. Envelope aperture 25 2.5. Multiresolution aperture 33 2.6. Summary 41 Bibliography 45 3. Finite-set signal processing, Ronald K. Pearson and Moncef Gabbouj 49 3.1. Introduction 49 3.2. Fundamental notions 51 3.3. Characterization on finite sets 56 3.4. Filters on finite sets 68 3.5. Variations and extensions 73 3.6. Summary 74 Bibliography 75 4. Nonlinear signal modeling and structure selection with applications to genomics, Ioan Tabus, Jorma Rissanen, and Jaakko Astola 79 4.1. Introduction 79 4.2. Preliminaries: modeling and predicting gene expressions 80 4.3. Several classes of nonlinear functions and associated design methods 83 4.4. Normalized maximum likelihood models for a class of Boolean regressor models 92 4.5. Summary 100 Bibliography 100 5. Nonlinear methods for speech analysis and synthesis, Steve McLaughlin and Petros Maragos 103 5.1. Introduction 103 5.2. What nonlinear methods might we use? 108 5.3. Summary 136 Bibliography 136 6. Communication system nonlinearities: challenges and some solutions, G. Tong Zhou, Hua Qian, and Ning Chen 141 6.1. Introduction 141 6.2. Nonlinear communication system concepts 142 6.3. Nonlinear distortions 150 6.4. Digital baseband predistortion linearization 156 6.5. Summary 164 Bibliography 165 7. Nonlinear multichannel active noise control, Giovanni L. Sicuranza and Alberto Carini 169 7.1. Introduction 169 7.2. The active noise control scenario 171 7.3. Nonlinear active noise controllers 184 7.4. A class of nonlinear feedforward active noise controllers 187 7.5. Simulation results 195 7.6. Current work and future developments 198 7.7. Summary 200 Bibliography 200 8. Chaotic sequences for digital watermarking, Nikos Nikolaidis, Anastasios Tefas, and Ioannis Pitas 205 8.1. Introduction 205 8.2. Correlation-based watermarking schemes employing Markov chaotic sequences 207 8.3. Watermark generation by chaotic mixing 229 8.4. Other applications of chaotic systems in digital watermarking 235 8.5. Summary 235 Bibliography 236 9. Modeling of evolving textures using granulometries, A. J. Gray, S. Marshall, and J. McKenzie 239 9.1. Introduction 239 9.2. Textures and texture analysis 239 9.3. Granulometries 245 9.4. Parallel evolution functions 249 9.5. Application to corrosion images 252 9.6. Modeling the texture 254 9.7. Summary 263 Bibliography 266 10. Multichannel weighted medians, Yinbo Li and Gonzalo R. Arce 273 10.1. Introduction 273 10.2. Multichannel weighted median filtering structures 275 10.3. Filter optimization 279 10.4. Complex multichannelWMs and their optimization 285 10.5. Simulations 290 10.6. Summary 297 Bibliography 298 11. Color image processing: problems, progress, and perspectives, E. R. Davies and D. Charles 301 11.1. Introduction 301 11.2. The color problem 303 11.3. Linear versus nonlinear processing 303 11.4. Color filtering 305 11.5. Color bleeding 306 11.6. The mode filter 310 11.7. Modern "switched" noise suppression filters 313 11.8. Filters with adjustable parameters 315 11.9. Distortions produced by median and other filters 316 11.10. Review of other color work 322 11.11. Summary 325 Bibliography 326 12. Nonlinear edge detection in color images, Adrian N. Evans 329 12.1. Introduction 329 12.2. Color edge detection 330 12.3. Color spaces and distance measures 331 12.4. Color edge detectors based on vector di.erences 333 12.5. Vector order statistics color edge detectors 337 12.6. Color morphological gradient operators 340 12.7. Results and evaluation 343 12.8. Summary 351 Bibliography 353 Index 357

About the Author :
Giovanni L. Sicuranza is Professor of Signal and Image Processing and head of the Image Processing Laboratory at the Dipartimento di Elettrotecnica Elettronica Informatica, University of Trieste (Italy), where he has given courses on analog circuits, digital circuits, and digital signal and image processing. He was also a teacher in European courses on image processing and analysis, and the organizer of the EURASIP course on "Linear and Nonlinear Filtering of Multidimensional Signals" (Trieste, Italy, 1990).His research interests include multidimensional digital filters, polynomial filters, processing of images and image sequences, image coding, and neural networks for signal processing. He has published a number of papers in international journals and conference proceedings. Stephen Marshall received a first-class honours degree in electrical and electronic engineering from the University of Nottingham in 1979 and a Ph.D. degree in image processing from University of Strathclyde in 1989. In between, he worked at Plessey Office Systems, Nottingham, University of Paisley, and the University of Rhode Island, USA. In recent years, his research activities have been focused in the area of nonlinear image processing. He has pioneered new design techniques for morphological filters based on a class of iterative search techniques known as genetic algorithms. The resulting filters have been applied as four-dimensional operators to successfully restore old film archive material. The work is now the subject of a Scottish Enterprise, Proof of Concept Program, to commercialise these techniques.