Nonlinear Signal Processing: A Statistical Approach focuses on unifying the study of a broad and important class of nonlinear signal processing algorithms which emerge from statistical estimation principles, and where the underlying signals are non-Gaussian, rather than Gaussian, processes. Notably, by concentrating on just two non-Gaussian models, a large set of tools is developed that encompass a large portion of the nonlinear signal processing tools proposed in the literature over the past several decades. Key features include: * Numerous problems at the end of each chapter to aid development and understanding * Examples and case studies provided throughout the book in a wide range of applications bring the text to life and place the theory into context * A set of 60+ MATLAB software m-files allowing the reader to quickly design and apply any of the nonlinear signal processing algorithms described in the book to an application of interest is available on the accompanying FTP site.

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 nonl

This state-of-the-art book deals with the most important aspects of non-linear imaging challenges. The need for engineering and mathematical methods is essential for defining non-linear effects involved in such areas as computer vision, optical imaging, computer pattern recognition, and industrial automation challenges. - Presents the latest developments in a variety of filter design techniques and algorithms - Contains essential information for development of Human Vision Systems (HVS) - Provides foundations for digital imaging and image capture technology

Image compression, the Navier-Stokes equations, and detection of gravitational waves are three seemingly unrelated scientific problems that, remarkably, can be studied from one perspective. The notion that unifies the three problems is that of ``oscillating patterns'', which are present in many natural images, help to explain nonlinear equations, and are pivotal in studying chirps and frequency-modulated signals. The first chapter of this book considers image processing, moreprecisely algorithms of image compression and denoising. This research is motivated in particular by the new standard for compression of still images known as JPEG-2000. The second chapter has new results on the Navier-Stokes and other nonlinear evolution equations. Frequency-modulated signals and theiruse in the detection of gravitational waves are covered in the final chapter. In the book, the author describes both what the oscillating patterns are and the mathematics necessary for their analysis. It turns out that this mathematics involves new properties of various Besov-type function spaces and leads to many deep results, including new generalizations of famous Gagliardo-Nirenberg and Poincare inequalities. This book is based on the ``Dean Jacqueline B. Lewis Memorial Lectures'' given bythe author at Rutgers University. It can be used either as a textbook in studying applications of wavelets to image processing or as a supplementary resource for studying nonlinear evolution equations or frequency-modulated signals. Most of the material in the book did not appear previously inmonograph literature.

From a strict semantic point of view, nonlinear image processing encompasses all image processing that is not based on linear operators; however, from a practical, evolutionary point of view, the name itself is usually associated with the study of nonlinear filters, mainly the deterministic and nondeterministic analysis and design of logic-based operators. This Tutorial Text volume explores logic-based operators with emphasis on representation, design, and statistical optimization of nonlinear filters.

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.

Compiled from papers presented at the 11th Annual Florida Workshop in Nonlinear Astronomy and Physics - Nonlinear Signal and Image Analysis, this work focuses on recent developments in time series and image processing techniques, as well as the physics that can be extracted using these techniques. It offers alternatives to conventional linear techniques, especially where chaos plays a role, and covers wavelet analysis, non-linear time-series analysis, neural networks, and spatial structures.

This unique text/reference presents a fresh look at nonlinear processing through nonlinear eigenvalue analysis, highlighting how one-homogeneous convex functionals can induce nonlinear operators that can be analyzed within an eigenvalue framework. The text opens with an introduction to the mathematical background, together with a summary of classical variational algorithms for vision. This is followed by a focus on the foundations and applications of the new multi-scale representation based on non-linear eigenproblems. The book then concludes with a discussion of new numerical techniques for finding nonlinear eigenfunctions, and promising research directions beyond the convex case. Topics and features: introduces the classical Fourier transform and its associated operator and energy, and asks how these concepts can be generalized in the nonlinear case; reviews the basic mathematical notion, briefly outlining the use of variational and flow-based methods to solve image-processing and computer vision algorithms; describes the properties of the total variation (TV) functional, and how the concept of nonlinear eigenfunctions relate to convex functionals; provides a spectral framework for one-homogeneous functionals, and applies this framework for denoising, texture processing and image fusion; proposes novel ways to solve the nonlinear eigenvalue problem using special flows that converge to eigenfunctions; examines graph-based and nonlocal methods, for which a TV eigenvalue analysis gives rise to strong segmentation, clustering and classification algorithms; presents an approach to generalizing the nonlinear spectral concept beyond the convex case, based on pixel decay analysis; discusses relations to other branches of image processing, such as wavelets and dictionary based methods. This original work offers fascinating new insights into established signal processing techniques, integrating deep mathematical concepts from a range of different fields, which will be of great interest to all researchers involved with image processing and computer vision applications, as well as computations for more general scientific problems.