In the past few years we have written and edited several books in the area of acousticandspeechsignalprocessing. Thereasonbehindthisendeavoristhat there were almost no books available in the literature when we ?rst started while there was (and still is) a real need to publish manuscripts summarizing the most useful ideas, concepts, results, and state-of-the-art algorithms in this important area of research. According to all the feedback we have received so far, we can say that we were right in doing this. Recently, several other researchers have followed us in this journey and have published interesting books with their own visions and perspectives. The idea of writing a book on Microphone Array Signal Processing comes from discussions we have had with many colleagues and friends. As a c- sequence of these discussions, we came up with the conclusion that, again, there is an urgent need for a monograph that carefully explains the theory and implementation of microphone arrays. While there are many manuscripts on antenna arrays from a narrowband perspective (narrowband signals and narrowband processing), the literature is quite scarce when it comes to s- sor arrays explained from a truly broadband perspective. Many algorithms for speech applications were simply borrowed from narrowband antenna - rays. However, a direct application of narrowband ideas to broadband speech processing may not be necessarily appropriate and can lead to many m- understandings.

Biomedical / Electrical Engineering Nonlinear Biomedical Signal Processing Volume II: Dynamic Analysis and Modeling A volume in the IEEE Press Series on Biomedical Engineering Metin Akay, Series Editor Featuring current contributions by experts in signal processing and biomedical engineering, this book introduces the concepts, recent advances, and implementations of nonlinear dynamic analysis methods. Together with Volume I in this series, this book provides comprehensive coverage of nonlinear signal and image processing techniques. Nonlinear Biomedical Signal Processing: Volume II combines analytical and biological expertise in the original mathematical simulation and modeling of physiological systems. Detailed discussions of the analysis of steady-state and dynamic systems, discrete-time system theory, and discrete modeling of continuous-time systems are provided. Biomedical examples include the analysis of the respiratory control system, the dynamics of cardiac muscle and the cardiorespiratory function, and neural firing patterns in auditory and vision systems. Examples include relevant MATLAB(r) and Pascal programs. Topics covered include:
* Nonlinear dynamics
* Behavior and estimation
* Modeling of biomedical signals and systems
* Heart rate variability measures, models, and signal assessments
* Origin of chaos in cardiovascular and gastric myoelectrical activity
* Measurement of spatio-temporal dynamics of human epileptic seizures.
A valuable reference book for medical researchers, medical faculty, and advanced graduate students, it is also essential reading for practicing biomedical engineers. Nonlinear Biomedical Signal Processing, Volume II is anexcellent companion to Dr. Akay's Nonlinear Biomedical Signal Processing, Volume I: Fuzzy Logic, Neural Networks, and New Algorithms.

This book is an accessible guide to adaptive signal processing methods that equips the reader with advanced theoretical and practical tools for the study and development of circuit structures and provides robust algorithms relevant to a wide variety of application scenarios. Examples include multimodal and multimedia communications, the biological and biomedical fields, economic models, environmental sciences, acoustics, telecommunications, remote sensing, monitoring and in general, the modeling and prediction of complex physical phenomena. The reader will learn not only how to design and implement the algorithms but also how to evaluate their performance for specific applications utilizing the tools provided. While using a simple mathematical language, the employed approach is very rigorous. The text will be of value both for research purposes and for courses of study.

This largely self-contained book on the theory of quantum information focuses on precise mathematical formulations and proofs of fundamental facts that form the foundation of the subject. It is intended for graduate students and researchers in mathematics, computer science, and theoretical physics seeking to develop a thorough understanding of key results, proof techniques, and methodologies that are relevant to a wide range of research topics within the theory of quantum information and computation. The book is accessible to readers with an understanding of basic mathematics, including linear algebra, mathematical analysis, and probability theory. An introductory chapter summarizes these necessary mathematical prerequisites, and starting from this foundation, the book includes clear and complete proofs of all results it presents. Each subsequent chapter includes challenging exercises intended to help readers to develop their own skills for discovering proofs concerning the theory of quantum information.

A timely and authoritative guide to the state of the art of wave scattering

Scattering of Electromagnetic Waves offers in three volumes a complete and up-to-date treatment of wave scattering by random discrete scatterers and rough surfaces. Written by leading scientists who have made important contributions to wave scattering over three decades, this new work explains the principles, methods, and applications of this rapidly expanding, interdisciplinary field. It covers both introductory and advanced material and provides students and researchers in remote sensing as well as imaging, optics, and electromagnetic theory with a one-stop reference to a wealth of current research results. Plus, Scattering of Electromagnetic Waves contains detailed discussions of both analytical and numerical methods, including cutting-edge techniques for the recovery of earth/land parametric information.

The three volumes are entitled respectively Theories and Applications, Numerical Simulation, and Advanced Topics. In the second volume, Numerical Simulations, Leung Tsang (University of Washington) Jin Au Kong (MIT), Kung-Hau Ding (Air Force Research Lab), and Chi On Ao (MIT) cover:

• Layered media simulations
• Rough surface and volume scattering simulations
• Dense media models and simulations
• Electromagnetic scattering by discrete scatterers and a buried object
• Scattering by vertical cylinders above a surface
• Electromagnetic waves scattering by vegetation
• Computational methods and programs used for performing various simulations

With the proliferation of mobile devices and hearing devices, including hearing aids and cochlear implants, there is a growing and pressing need to design algorithms that can improve speech intelligibility without sacrificing quality. Responding to this need, Speech Enhancement: Theory and Practice, Second Edition introduces readers to the basic problems of speech enhancement and the various algorithms proposed to solve these problems. Updated and expanded, this second edition of the bestselling textbook broadens its scope to include evaluation measures and enhancement algorithms aimed at improving speech intelligibility. Fundamentals, Algorithms, Evaluation, and Future Steps Organized into four parts, the book begins with a review of the fundamentals needed to understand and design better speech enhancement algorithms. The second part describes all the major enhancement algorithms and, because these require an estimate of the noise spectrum, also covers noise estimation algorithms. The third part of the book looks at the measures used to assess the performance, in terms of speech quality and intelligibility, of speech enhancement methods. It also evaluates and compares several of the algorithms. The fourth part presents binary mask algorithms for improving speech intelligibility under ideal conditions. In addition, it suggests steps that can be taken to realize the full potential of these algorithms under realistic conditions. What's New in This Edition Updates in every chapter A new chapter on objective speech intelligibility measures A new chapter on algorithms for improving speech intelligibility Real-world noise recordings (on downloadable resources) MATLAB (R) code for the implementation of intelligibility measures (on downloadable resources) MATLAB and C/C++ code for the implementation of algorithms to improve speech intelligibility (on downloadable resources) Valuable Insights from a Pioneer in Speech Enhancement Clear and concise, this book explores how human listeners compensate for acoustic noise in noisy environments. Written by a pioneer in speech enhancement and noise reduction in cochlear implants, it is an essential resource for anyone who wants to implement or incorporate the latest speech enhancement algorithms to improve the quality and intelligibility of speech degraded by noise. Includes downloadable resources with Code and Recordings The downloadable resources provide MATLAB implementations of representative speech enhancement algorithms as well as speech and noise databases for the evaluation of enhancement algorithms.

Probability and Random Processes, Second Edition presents pertinent applications to signal processing and communications, two areas of key interest to students and professionals in today's booming communications industry. The book includes unique chapters on narrowband random processes and simulation techniques. It also describes applications in digital communications, information theory, coding theory, image processing, speech analysis, synthesis and recognition, and others. Exceptional exposition and numerous worked out problems make this book extremely readable and accessible. The authors connect the applications discussed in class to the textbook. The new edition contains more real world signal processing and communications applications. It introduces the reader to the basics of probability theory and explores topics ranging from random variables, distributions and density functions to operations on a single random variable. There are also discussions on pairs of random variables; multiple random variables; random sequences and series; random processes in linear systems; Markov processes; and power spectral density. This book is intended for practicing engineers and students in graduate-level courses in the topic.

Data-driven discovery is revolutionizing how we model, predict, and control complex systems. Now with Python and MATLAB (R), this textbook trains mathematical scientists and engineers for the next generation of scientific discovery by offering a broad overview of the growing intersection of data-driven methods, machine learning, applied optimization, and classical fields of engineering mathematics and mathematical physics. With a focus on integrating dynamical systems modeling and control with modern methods in applied machine learning, this text includes methods that were chosen for their relevance, simplicity, and generality. Topics range from introductory to research-level material, making it accessible to advanced undergraduate and beginning graduate students from the engineering and physical sciences. The second edition features new chapters on reinforcement learning and physics-informed machine learning, significant new sections throughout, and chapter exercises. Online supplementary material - including lecture videos per section, homeworks, data, and code in MATLAB (R), Python, Julia, and R - available on databookuw.com.

In nonparametric and high-dimensional statistical models, the classical Gauss-Fisher-Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In a final chapter the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions. Winner of the 2017 PROSE Award for Mathematics.

This book introduces machine learning for readers with some background in basic linear algebra, statistics, probability, and programming. In a coherent statistical framework it covers a selection of supervised machine learning methods, from the most fundamental (k-NN, decision trees, linear and logistic regression) to more advanced methods (deep neural networks, support vector machines, Gaussian processes, random forests and boosting), plus commonly-used unsupervised methods (generative modeling, k-means, PCA, autoencoders and generative adversarial networks). Careful explanations and pseudo-code are presented for all methods. The authors maintain a focus on the fundamentals by drawing connections between methods and discussing general concepts such as loss functions, maximum likelihood, the bias-variance decomposition, ensemble averaging, kernels and the Bayesian approach along with generally useful tools such as regularization, cross validation, evaluation metrics and optimization methods. The final chapters offer practical advice for solving real-world supervised machine learning problems and on ethical aspects of modern machine learning.

Quickly Engages in Applying Algorithmic Techniques to Solve Practical Signal Processing Problems

With its active, hands-on learning approach, this text enables readers to master the underlying principles of digital signal processing and its many applications in industries such as digital television, mobile and broadband communications, and medical/scientific devices. Carefully developed MATLAB(R) examples throughout the text illustrate the mathematical concepts and use of digital signal processing algorithms. Readers will develop a deeper understanding of how to apply the algorithms by manipulating the codes in the examples to see their effect. Moreover, plenty of exercises help to put knowledge into practice solving real-world signal processing challenges.

Following an introductory chapter, the text explores:

Sampled signals and digital processing

Random signals

Representing signals and systems

Temporal and spatial signal processing

Frequency analysis of signals

Discrete-time filters and recursive filters

Each chapter begins with chapter objectives and an introduction. A summary at the end of each chapter ensures that one has mastered all the key concepts and techniques before progressing in the text. Lastly, appendices listing selected web resources, research papers, and related textbooks enable the investigation of individual topics in greater depth.

Upon completion of this text, readers will understand how to apply key algorithmic techniques to address practical signal processing problems as well as develop their own signal processing algorithms. Moreover, the text provides a solid foundation for evaluating and applying new digital processing signal techniques as they are developed.

With its exhaustive coverage of relevant theory, Signals and Systems Laboratory with MATLAB (R) is a powerful resource that provides simple, detailed instructions on how to apply computer methods to signals and systems analysis. Written for laboratory work in a course on signals and systems, this book presents a corresponding MATLAB implementation for each theoretical concept introduced, making it a powerful learning tool for engineers, scientists, and students alike. MATLAB code is used in problems and examples presented throughout the book. This code and other learning materials are available in a downloadable supplement. Due to the extensive-and truly unique-integration of MATLAB throughout this book, the authors provide a complete tutorial on use of the language for signals and systems analysis. With more than 5,000 lines of MATLAB code and more than 700 figures embedded in the text, the material teaches readers how to program in MATLAB and study signals and systems concepts at the same time, giving them the tools to harness the power of computers to quickly assess problems and then visualize their solutions. Among its many useful features, this book: Offers complete coverage of the signals and systems theory, starting with elementary signals and concluding with state-space modeling Contains more than 400 examples and chapter-end solved problems Executes commands one-by-one at the MATLAB command prompt, and results, along with comments, encouraging students to learn MATLAB on the fly Additional Pedagogical Features: A detailed MATLAB tutorial to introduce a beginner programmer to the language Laboratory exercises that give students hands-on experience and help professors organize a course laboratory component Presentation of continuous- and discrete-time in parallel fashion, effectively illustrating the similarities and differences between the two Step-by-step examples that present data in tabular format and usually offer several different solutions to each problem

Compiled from papers of the 4th Biennial Workshop on DSP (Digital Signal Processing) for In-Vehicle Systems and Safety this edited collection features world-class experts from diverse fields focusing on integrating smart in-vehicle systems with human factors to enhance safety in automobiles. "Digital Signal Processing for In-Vehicle Systems and Safety" presents new approaches on how to reduce driver inattention and prevent road accidents.

The material addresses DSP technologies in adaptive automobiles, in-vehicle dialogue systems, human machine interfaces, video and audio processing, and in-vehicle speech systems. The volume also features recent advances in Smart-Car technology, coverage of autonomous vehicles that drive themselves, and information on multi-sensor fusion for driver ID and robust driver monitoring.

"Digital Signal Processing for In-Vehicle Systems and Safety" is useful for engineering researchers, students, automotive manufacturers, government foundations and engineers working in the areas of control engineering, signal processing, audio-video processing, bio-mechanics, human factors and transportation engineering.

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This book focuses on broadband power amplifier design for wireless communication. Nonlinear model embedding is described as a powerful tool for designing broadband continuous Class-J and continuous class F power amplifiers. The authors also discuss various techniques for extending bandwidth of load modulation based power amplifiers, such as Doherty power amplifier and Chireix outphasing amplifiers. The book also covers recent trends on digital as well as analog techniques to enhance bandwidth and linearity in wireless transmitters. Presents latest trends in designing broadband power amplifiers; Covers latest techniques for using nonlinear model embedding in designing power amplifiers based on waveform engineering; Describes the latest techniques for extending bandwidth of load modulation based power amplifiers such as Doherty power amplifier and Chireix outphasing amplifiers; Includes coverage of hybrid analog/digital predistortion as wideband solution for wireless transmitters; Discusses recent trends on on-chip power amplifier design with GaN /GaAs MMICs for high frequency applications.

This book deals with the autoregressive method for digital processing of random oscillations. The method is based on a one-to-one transformation of the numeric factors of the Yule series model to linear elastic system characteristics. This parametric approach allowed to develop a formal processing procedure from the experimental data to obtain estimates of logarithmic decrement and natural frequency of random oscillations. A straightforward mathematical description of the procedure makes it possible to optimize a discretization of oscillation realizations providing efficient estimates. The derived analytical expressions for confidence intervals of estimates enable a priori evaluation of their accuracy. Experimental validation of the method is also provided. Statistical applications for the analysis of mechanical systems arise from the fact that the loads experienced by machineries and various structures often cannot be described by deterministic vibration theory. Therefore, a sufficient description of real oscillatory processes (vibrations) calls for the use of random functions. In engineering practice, the linear vibration theory (modeling phenomena by common linear differential equations) is generally used. This theory's fundamental concepts such as natural frequency, oscillation decrement, resonance, etc. are credited for its wide use in different technical tasks. In technical applications two types of research tasks exist: direct and inverse. The former allows to determine stochastic characteristics of the system output X(t) resulting from a random process E(t) when the object model is considered known. The direct task enables to evaluate the effect of an operational environment on the designed object and to predict its operation under various loads. The inverse task is aimed at evaluating the object model on known processes E(t) and X(t), i.e. finding model (equations) factors. This task is usually met at the tests of prototypes to identify (or verify) its model experimentally. To characterize random processes a notion of "shaping dynamic system" is commonly used. This concept allows to consider the observing process as the output of a hypothetical system with the input being stationary Gauss-distributed ("white") noise. Therefore, the process may be exhaustively described in terms of parameters of that system. In the case of random oscillations, the "shaping system" is an elastic system described by the common differential equation of the second order: X (t)+2hX (t)+ _0^2 X(t)=E(t), where 0 = 2 / 0 is the natural frequency, T0 is the oscillation period, and h is a damping factor. As a result, the process X(t) can be characterized in terms of the system parameters - natural frequency and logarithmic oscillations decrement = hT0 as well as the process variance. Evaluation of these parameters is subjected to experimental data processing based on frequency or time-domain representations of oscillations. It must be noted that a concept of these parameters evaluation did not change much during the last century. For instance, in case of the spectral density utilization, evaluation of the decrement values is linked with bandwidth measurements at the points of half-power of the observed oscillations. For a time-domain presentation, evaluation of the decrement requires measuring covariance values delayed by a time interval divisible by T0. Both estimation procedures are derived from a continuous description of research phenomena, so the accuracy of estimates is linked directly to the adequacy of discrete representation of random oscillations. This approach is similar a concept of transforming differential equations to difference ones with derivative approximation by corresponding finite differences. The resulting discrete model, being an approximation, features a methodical error which can be decreased but never eliminated. To render such a presentation more accurate it is imperative to decrease the discretization interval and to increase realization size growing requirements for computing power. The spectral density and covariance function estimates comprise a non-parametric (non-formal) approach. In principle, any non-formal approach is a kind of art i.e. the results depend on the performer's skills. Due to interference of subjective factors in spectral or covariance estimates of random signals, accuracy of results cannot be properly determined or justified. To avoid the abovementioned difficulties, the application of linear time-series models with well-developed procedures for parameter estimates is more advantageous. A method for the analysis of random oscillations using a parametric model corresponding discretely (no approximation error) with a linear elastic system is developed and presented in this book. As a result, a one-to-one transformation of the model's numerical factors to logarithmic decrement and natural frequency of random oscillations is established. It allowed to develop a formal processing procedure from experimental data to obtain the estimates of and 0. The proposed approach allows researchers to replace traditional subjective techniques by a formal processing procedure providing efficient estimates with analytically defined statistical uncertainties.

Artificial neural networks can be employed to solve a wide spectrum of problems in optimization, parallel computing, matrix algebra and signal processing. Taking a computational approach, this book explains how ANNs provide solutions in real time, and allow the visualization and development of new techniques and architectures. Features include a guide to the fundamental mathematics of neurocomputing, a review of neural network models and an analysis of their associated algorithms, and state-of-the-art procedures to solve optimization problems. Computer simulation programs MATLAB, TUTSIM and SPICE illustrate the validity and performance of the algorithms and architectures described. The authors encourage the reader to be creative in visualizing new approaches and detail how other specialized computer programs can evaluate performance. Each chapter concludes with a short bibliography. Illustrative worked examples, questions and problems assist self study. The authors' self-contained approach will appeal to a wide range of readers, including professional engineers working in computing, optimization, operational research, systems identification and control theory. Undergraduate and postgraduate students in computer science, electrical and electronic engineering will also find this text invaluable. In particular, the text will be ideal to supplement courses in circuit analysis and design, adaptive systems, control systems, signal processing and parallel computing.

A timely and authoritative guide to the state of the art of wave scattering

Scattering of Electromagnetic Waves offers in three volumes a complete and up-to-date treatment of wave scattering by random discrete scatterers and rough surfaces. Written by leading scientists who have made important contributions to wave scattering over three decades, this new work explains the principles, methods, and applications of this rapidly expanding, interdisciplinary field. It covers both introductory and advanced material and provides students and researchers in remote sensing as well as imaging, optics, and electromagnetic theory with a one-stop reference to a wealth of current research results. Plus, Scattering of Electromagnetic Waves contains detailed discussions of both analytical and numerical methods, including cutting-edge techniques for the recovery of earth/land parametric information.

The three volumes are entitled respectively Theories and Applications, Numerical Simulation, and Advanced Topics. In the third volume, Advanced Topics, Leung Tsang (University of Washington) and Jin Au Kong (MIT), cover:

• Two-dimensional random rough surface scattering
• Kirchhoff and related methods for rough surface scattering
• Analytic theory of volume scattering based on cascading of layers
• Analytic wave theory for medium with permittivity fluctuations
• Multiple scattering theory for discrete scatterers
• Quasicrystalline approximation in dense media scattering
• Dense media scattering
• Backscattering enhancement

Learn to solve the unprecedented challenges facing Online Learning and Adaptive Signal Processing in this concise, intuitive text. The ever-increasing amount of data generated every day requires new strategies to tackle issues such as: combining data from a large number of sensors; improving spectral usage, utilizing multiple-antennas with adaptive capabilities; or learning from signals placed on graphs, generating unstructured data. Solutions to all of these and more are described in a condensed and unified way, enabling you to expose valuable information from data and signals in a fast and economical way. The up-to-date techniques explained here can be implemented in simple electronic hardware, or as part of multi-purpose systems. Also featuring alternative explanations for online learning, including newly developed methods and data selection, and several easily implemented algorithms, this one-of-a-kind book is an ideal resource for graduate students, researchers, and professionals in online learning and adaptive filtering.

Based on years of instruction and field expertise, this volume offers the necessary tools to understand all scientific, computational, and technological aspects of speech processing. The book emphasizes mathematical abstraction, the dynamics of the speech process, and the engineering optimization practices that promote effective problem solving in this area of research and covers many years of the authors' personal research on speech processing. Speech Processing helps build valuable analytical skills to help meet future challenges in scientific and technological advances in the field and considers the complex transition from human speech processing to computer speech processing.

Contents:
PartI: Multidimensional Systems - General 1. Two Decades of Multidimensional Systems Research and Future Trends 2. MATLAB Package for n-D Sampling-Based Modelling of Nonlinear Systems 3. Behaviours, Modules, and Duality. Part II: Control of Multidimensional Systems and Applications 4. Output Feedback Stabilizability and Stabilization of Linear n-D Systems 5. A Review of n-D System Control Theory in a Certain Practical Sense 6. Two Decades of Research on Linear Repetitive Processes 7. Analysis and Control of Discrete Linear Repetitive Processes with Dynamic Boundary Conditions 8. Entire Function Methods for Optimisation Problems in Continuous-Discrete 2D Control Systems 9. Existence of an Optimal Solution for a Continuous Roesser Problem with a Terminal Condition. Part III: Multidimensional Circuits and Signal Processing 10. On The Structure of Linear Phase Perfect Reconstruction Quincunx Filter Banks 11. Deadbands in m-D Delta Operator Based Digital Filters with Floating Point Arithmetic 12. Cascade Synthesis of Two-Variable Lossless Two-Port Networks with Lumped Elements and Transmission Lines: A Semi-Analytic Procedure 13. Reconstruction of Positron Emission Tomography Images by Using MAP Estimation 14. Inspection of Fixing Devices of Railroad Lines Using Image Processing Algorithms 15. Increase of Frame Rate in Virtual Environments by Using 2D Image Warping

"In 1971 Dr. Paul C. Lauterbur pioneered spatial information encoding principles that made image formation possible by using magnetic resonance signals. Now Lauterbur, ""father of the MRI,"" and Dr. Zhi-Pei Liang have co-authored the first engineering textbook on magnetic resonance imaging. This long-awaited, definitive text will help undergraduate and graduate students of biomedical engineering, biomedical imaging scientists, radiologists, and electrical engineers gain an in-depth understanding of MRI principles. The authors use a signal processing approach to describe the fundamentals of magnetic resonance imaging. You will find a clear and rigorous discussion of these carefully selected essential topics: * Mathematical fundamentals Signal generation and detection principles* Signal characteristics* Signal localization principles* Image reconstruction techniques* Image contrast mechanisms Image resolution, noise, and artifacts* Fast-scan imaging* Constrained reconstruction. Complete with a comprehensive set of examples and homework problems, PRINCIPLES OF MAGNETIC RESONANCE IMAGING is the must-read book to improve your knowledge of this revolutionary technique. For more information on the IEEE Press Series in Biomedical Engineering edited by Metin Akay, go to http://www caip.rutgers.edu/ per cent7Eakay/book/ Professors: To request an examination copy simply e-mail [email protected]." Sponsored by: IEEE Engineering in Medicine and Biology Society.

This is the third volume in a trilogy on modern Signal Processing. The three books provide a concise exposition of signal processing topics, and a guide to support individual practical exploration based on MATLAB programs. This book includes MATLAB codes to illustrate each of the main steps of the theory, offering a self-contained guide suitable for independent study. The code is embedded in the text, helping readers to put into practice the ideas and methods discussed. The book primarily focuses on filter banks, wavelets, and images. While the Fourier transform is adequate for periodic signals, wavelets are more suitable for other cases, such as short-duration signals: bursts, spikes, tweets, lung sounds, etc. Both Fourier and wavelet transforms decompose signals into components. Further, both are also invertible, so the original signals can be recovered from their components. Compressed sensing has emerged as a promising idea. One of the intended applications is networked devices or sensors, which are now becoming a reality; accordingly, this topic is also addressed. A selection of experiments that demonstrate image denoising applications are also included. In the interest of reader-friendliness, the longer programs have been grouped in an appendix; further, a second appendix on optimization has been added to supplement the content of the last chapter.

An intuitive and accessible text explaining the fundamentals and applications of graph signal processing. Requiring only an elementary understanding of linear algebra, it covers both basic and advanced topics, including node domain processing, graph signal frequency, sampling, and graph signal representations, as well as how to choose a graph. Understand the basic insights behind key concepts and learn how graphs can be associated to a range of specific applications across physical, biological and social networks, distributed sensor networks, image and video processing, and machine learning. With numerous exercises and Matlab examples to help put knowledge into practice, and a solutions manual available online for instructors, this unique text is essential reading for graduate and senior undergraduate students taking courses on graph signal processing, signal processing, information processing, and data analysis, as well as researchers and industry professionals.

High-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions. Drawing on ideas from probability, analysis, and geometry, it lends itself to applications in mathematics, statistics, theoretical computer science, signal processing, optimization, and more. It is the first to integrate theory, key tools, and modern applications of high-dimensional probability. Concentration inequalities form the core, and it covers both classical results such as Hoeffding's and Chernoff's inequalities and modern developments such as the matrix Bernstein's inequality. It then introduces the powerful methods based on stochastic processes, including such tools as Slepian's, Sudakov's, and Dudley's inequalities, as well as generic chaining and bounds based on VC dimension. A broad range of illustrations is embedded throughout, including classical and modern results for covariance estimation, clustering, networks, semidefinite programming, coding, dimension reduction, matrix completion, machine learning, compressed sensing, and sparse regression.

Recovering the phase of the Fourier transform is a ubiquitous problem in imaging applications from astronomy to nanoscale X-ray diffraction imaging. Despite the efforts of a multitude of scientists, from astronomers to mathematicians, there is, as yet, no satisfactory theoretical or algorithmic solution to this class of problems. Written for mathematicians, physicists and engineers working in image analysis and reconstruction, this book introduces a conceptual, geometric framework for the analysis of these problems, leading to a deeper understanding of the essential, algorithmically independent, difficulty of their solutions. Using this framework, the book studies standard algorithms and a range of theoretical issues in phase retrieval and provides several new algorithms and approaches to this problem with the potential to improve the reconstructed images. The book is lavishly illustrated with the results of numerous numerical experiments that motivate the theoretical development and place it in the context of practical applications.