Nonlinear Signal And Image Processing

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.

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 signal processing (SP) landscape has been enriched by recent advances in artificial intelligence (AI) and machine learning (ML), yielding new tools for signal estimation, classification, prediction, and manipulation. Layered signal representations, nonlinear function approximation and nonlinear signal prediction are now feasible at very large scale in both dimensionality and data size. These are leading to significant performance gains in a variety of long-standing problem domains like speech and image analysis as well as providing the ability to construct new classes of nonlinear functions (e.g., fusion, nonlinear filtering). This book will help academics, researchers, developers, graduate and undergraduate students to comprehend complex SP data across a wide range of topical application areas such as social multimedia data collected from social media networks, medical imaging data, data from Covid tests, etc. This book focuses on AI utilization in the speech, image, communications and virtual reality domains.

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.

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.