Applied And Computational Harmonic Analysis

applied and computational harmonic analysis: Computational Signal Processing with Wavelets Anthony Teolis, 2017-10-02 This unique resource examines the conceptual, computational, and practical aspects of applied signal processing using wavelets. With this book, readers will understand and be able to use the power and utility of new wavelet methods in science and engineering problems and analysis. The text is written in a clear, accessible style avoiding unnecessary abstractions and details. From a computational perspective, wavelet signal processing algorithms are presented and applied to signal compression, noise suppression, and signal identification. Numerical illustrations of these computational techniques are further provided with interactive software (MATLAB code) that is available on the World Wide Web. Topics and Features Continuous wavelet and Gabor transforms Frame-based theory of discretization and reconstruction of analog signals is developed New and efficient overcomplete wavelet transform is introduced and applied Numerical illustrations with an object-oriented computational perspective using the Wavelet Signal Processing Workstation (MATLAB code) available This book is an excellent resource for information and computational tools needed to use wavelets in many types of signal processing problems. Graduates, professionals, and practitioners in engineering, computer science, geophysics, and applied mathematics will benefit from using the book and software tools. The present, softcover reprint is designed to make this classic textbook available to a wider audience. A self-contained text that is theoretically rigorous while maintaining contact with interesting applications. A particularly noteworthy topic...is a class of ‘overcomplete wavelets’. These functions are not orthonormal and they lead to many useful results. —Journal of Mathematical Psychology
applied and computational harmonic analysis: Harmonic Analysis and Applications John J. Benedetto, 1996-07-29 Harmonic analysis plays an essential role in understanding a host of engineering, mathematical, and scientific ideas. In Harmonic Analysis and Applications, the analysis and synthesis of functions in terms of harmonics is presented in such a way as to demonstrate the vitality, power, elegance, usefulness, and the intricacy and simplicity of the subject. This book is about classical harmonic analysis - a textbook suitable for students, and an essay and general reference suitable for mathematicians, physicists, and others who use harmonic analysis. Throughout the book, material is provided for an upper level undergraduate course in harmonic analysis and some of its applications. In addition, the advanced material in Harmonic Analysis and Applications is well-suited for graduate courses. The course is outlined in Prologue I. This course material is excellent, not only for students, but also for scientists, mathematicians, and engineers as a general reference. Chapter 1 covers the Fourier analysis of integrable and square integrable (finite energy) functions on R. Chapter 2 of the text covers distribution theory, emphasizing the theory's useful vantage point for dealing with problems and general concepts from engineering, physics, and mathematics. Chapter 3 deals with Fourier series, including the Fourier analysis of finite and infinite sequences, as well as functions defined on finite intervals. The mathematical presentation, insightful perspectives, and numerous well-chosen examples and exercises in Harmonic Analysis and Applications make this book well worth having in your collection.
applied and computational harmonic analysis: Linear Algebra, Signal Processing, and Wavelets - A Unified Approach Øyvind Ryan, 2019-03-05 This book offers a user friendly, hands-on, and systematic introduction to applied and computational harmonic analysis: to Fourier analysis, signal processing and wavelets; and to their interplay and applications. The approach is novel, and the book can be used in undergraduate courses, for example, following a first course in linear algebra, but is also suitable for use in graduate level courses. The book will benefit anyone with a basic background in linear algebra. It defines fundamental concepts in signal processing and wavelet theory, assuming only a familiarity with elementary linear algebra. No background in signal processing is needed. Additionally, the book demonstrates in detail why linear algebra is often the best way to go. Those with only a signal processing background are also introduced to the world of linear algebra, although a full course is recommended. The book comes in two versions: one based on MATLAB, and one on Python, demonstrating the feasibility and applications of both approaches. Most of the MATLAB code is available interactively. The applications mainly involve sound and images. The book also includes a rich set of exercises, many of which are of a computational nature.
applied and computational harmonic analysis: Harmonic Analysis for Engineers and Applied Scientists Gregory S. Chirikjian, Alexander B. Kyatkin, 2016-07-20 Although the Fourier transform is among engineering's most widely used mathematical tools, few engineers realize that the extension of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. This self-contained approach, geared toward readers with a standard background in engineering mathematics, explores the widest possible range of applications to fields such as robotics, mechanics, tomography, sensor calibration, estimation and control, liquid crystal analysis, and conformational statistics of macromolecules. Harmonic analysis is explored in terms of particular Lie groups, and the text deals with only a limited number of proofs, focusing instead on specific applications and fundamental mathematical results. Forming a bridge between pure mathematics and the challenges of modern engineering, this updated and expanded volume offers a concrete, accessible treatment that places the general theory in the context of specific groups.
applied and computational harmonic analysis: An Introduction to Harmonic Analysis Yitzhak Katznelson, 1968
applied and computational harmonic analysis: Functions, Spaces, and Expansions Ole Christensen, 2010-05-27 This graduate-level textbook is a detailed exposition of key mathematical tools in analysis aimed at students, researchers, and practitioners across science and engineering. Every topic covered has been specifically chosen because it plays a key role outside the field of pure mathematics. Although the treatment of each topic is mathematical in nature, and concrete applications are not delineated, the principles and tools presented are fundamental to exploring the computational aspects of physics and engineering. Readers are expected to have a solid understanding of linear algebra, in Rn and in general vector spaces. Familiarity with the basic concepts of calculus and real analysis, including Riemann integrals and infinite series of real or complex numbers, is also required.
applied and computational harmonic analysis: Excursions in Harmonic Analysis, Volume 6 Matthew Hirn, Shidong Li, Kasso A. Okoudjou, Sandra Saliani, Özgür Yilmaz, 2021-09-01 John J. Benedetto has had a profound influence not only on the direction of harmonic analysis and its applications, but also on the entire community of people involved in the field. The chapters in this volume – compiled on the occasion of his 80th birthday – are written by leading researchers in the field and pay tribute to John’s many significant and lasting achievements. Covering a wide range of topics in harmonic analysis and related areas, these chapters are organized into four main parts: harmonic analysis, wavelets and frames, sampling and signal processing, and compressed sensing and optimization. An introductory chapter also provides a brief overview of John’s life and mathematical career. This volume will be an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics.
applied and computational harmonic analysis: Computational Analysis George A. Anastassiou, Oktay Duman, 2018-05-30 Featuring the clearly presented and expertly-refereed contributions of leading researchers in the field of approximation theory, this volume is a collection of the best contributions at the Third International Conference on Applied Mathematics and Approximation Theory, an international conference held at TOBB University of Economics and Technology in Ankara, Turkey, on May 28-31, 2015. The goal of the conference, and this volume, is to bring together key work from researchers in all areas of approximation theory, covering topics such as ODEs, PDEs, difference equations, applied analysis, computational analysis, signal theory, positive operators, statistical approximation, fuzzy approximation, fractional analysis, semigroups, inequalities, special functions and summability. These topics are presented both within their traditional context of approximation theory, while also focusing on their connections to applied mathematics. As a result, this collection will be an invaluable resource for researchers in applied mathematics, engineering and statistics.
applied and computational harmonic analysis: Computational Methods for Inverse Problems Curtis R. Vogel, 2002-01-01 Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
applied and computational harmonic analysis: Applied Analysis Cornelius Lanczos, 1988-01-01 Classic work on analysis and design of finite processes for approximating solutions of analytical problems. Features algebraic equations, matrices, harmonic analysis, quadrature methods, and much more.
applied and computational harmonic analysis: Wavelets Stephane Jaffard, Yves Meyer, Robert D. Ryan, 2001-01-01 This long-awaited update of Meyer's Wavelets: Algorithms and Applications includes completely new chapters on four topics: wavelets and the study of turbulence, wavelets and fractals (which includes an analysis of Riemann's nondifferentiable function), data compression, and wavelets in astronomy. The chapter on data compression was the original motivation for this revised edition, and it contains up-to-date information on the interplay between wavelets and nonlinear approximation. The other chapters have been rewritten with comments, references, historical notes, and new material. Four appendices have been added: a primer on filters, key results (with proofs) about the wavelet transform, a complete discussion of a counterexample to the Marr-Mallat conjecture on zero-crossings, and a brief introduction to H?lder and Besov spaces. In addition, all of the figures have been redrawn, and the references have been expanded to a comprehensive list of over 260 entries. The book includes several new results that have not appeared elsewhere.
applied and computational harmonic analysis: Harmonic and Applied Analysis Stephan Dahlke, Filippo De Mari, Philipp Grohs, Demetrio Labate, 2015-09-12 This contributed volume explores the connection between the theoretical aspects of harmonic analysis and the construction of advanced multiscale representations that have emerged in signal and image processing. It highlights some of the most promising mathematical developments in harmonic analysis in the last decade brought about by the interplay among different areas of abstract and applied mathematics. This intertwining of ideas is considered starting from the theory of unitary group representations and leading to the construction of very efficient schemes for the analysis of multidimensional data. After an introductory chapter surveying the scientific significance of classical and more advanced multiscale methods, chapters cover such topics as An overview of Lie theory focused on common applications in signal analysis, including the wavelet representation of the affine group, the Schrödinger representation of the Heisenberg group, and the metaplectic representation of the symplectic group An introduction to coorbit theory and how it can be combined with the shearlet transform to establish shearlet coorbit spaces Microlocal properties of the shearlet transform and its ability to provide a precise geometric characterization of edges and interface boundaries in images and other multidimensional data Mathematical techniques to construct optimal data representations for a number of signal types, with a focus on the optimal approximation of functions governed by anisotropic singularities. A unified notation is used across all of the chapters to ensure consistency of the mathematical material presented. Harmonic and Applied Analysis: From Groups to Signals is aimed at graduate students and researchers in the areas of harmonic analysis and applied mathematics, as well as at other applied scientists interested in representations of multidimensional data. It can also be used as a textbook for graduate courses in applied harmonic analysis.
applied and computational harmonic analysis: Classical and Multilinear Harmonic Analysis Camil Muscalu, Wilhelm Schlag, 2013-01-31 This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.
applied and computational harmonic analysis: Locally Convex Spaces and Harmonic Analysis: An Introduction Philippe G. Ciarlet, 2021-08-10 This self-contained textbook covers the fundamentals of two basic topics of linear functional analysis: locally convex spaces and harmonic analysis. Readers will find detailed introductions to topological vector spaces, distribution theory, weak topologies, the Fourier transform, the Hilbert transform, and Calderón–Zygmund singular integrals. An ideal introduction to more advanced texts, the book complements Ciarlet’s Linear and Nonlinear Functional Analysis with Applications (SIAM), in which these two topics were not treated. Pedagogical features such as detailed proofs and 93 problems make the book ideal for a one-semester first-year graduate course or for self-study. The book is intended for advanced undergraduates and first-year graduate students and researchers. It is appropriate for courses on functional analysis, distribution theory, Fourier transform, and harmonic analysis.
applied and computational harmonic analysis: Fourier Analysis and Its Applications G. B. Folland, 2009 This book presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. It includes material on Bessel functions, orthogonal polynomials, and Laplace transforms, and it concludes with chapters on generalized functions and Green's functions for ordinary and partial differential equations. The book deals almost exclusively with aspects of these subjects that are useful in physics and engineering, and includes a wide variety of applications. On the theoretical side, it uses ideas from modern analysis to develop the concepts and reasoning behind the techniques without getting bogged down in the technicalities of rigorous proofs.
applied and computational harmonic analysis: Discrete Tomography Gabor T. Herman, Attila Kuba, 1999-11 Goals of the Book Overthelast thirty yearsthere has been arevolutionindiagnostic radiology as a result oftheemergenceofcomputerized tomography (CT), which is the process of obtaining the density distribution within the human body from multiple x-ray projections. Since an enormous variety of possible density values may occur in the body, a large number of projections are necessary to ensure the accurate reconstruction oftheir distribution. There are other situations in which we desire to reconstruct an object from its projections, but in which we know that the object to be recon structed has only a small number of possible values. For example, a large fraction of objects scanned in industrial CT (for the purpose of nonde structive testing or reverse engineering) are made of a single material and so the ideal reconstruction should contain only two values: zero for air and the value associated with the material composing the object. Similar as sumptions may even be made for some specific medical applications; for example, in angiography ofthe heart chambers the value is either zero (in dicating the absence of dye) or the value associated with the dye in the chamber. Another example arises in the electron microscopy of biological macromolecules, where we may assume that the object to be reconstructed is composed of ice, protein, and RNA. One can also apply electron mi croscopy to determine the presenceor absence ofatoms in crystallinestruc tures, which is again a two-valued situation.
applied and computational harmonic analysis: Special Functions of Mathematical (Geo-)Physics Willi Freeden, Martin Gutting, 2013-02-15 Special functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A good understanding of special functions provides the capacity to recognize the causality between the abstractness of the mathematical concept and both the impact on and cross-sectional importance to the scientific reality. The special functions to be discussed in this monograph vary greatly, depending on the measurement parameters examined (gravitation, electric and magnetic fields, deformation, climate observables, fluid flow, etc.) and on the respective field characteristic (potential field, diffusion field, wave field). The differential equation under consideration determines the type of special functions that are needed in the desired reduction process. Each chapter closes with exercises that reflect significant topics, mostly in computational applications. As a result, readers are not only directly confronted with the specific contents of each chapter, but also with additional knowledge on mathematical fields of research, where special functions are essential to application. All in all, the book is an equally valuable resource for education in geomathematics and the study of applied and harmonic analysis. Students who wish to continue with further studies should consult the literature given as supplements for each topic covered in the exercises.
applied and computational harmonic analysis: Selected Unsolved Problems in Coding Theory David Joyner, Jon-Lark Kim, 2011-08-26 Using an original mode of presentation, and emphasizing the computational nature of the subject, this book explores a number of the unsolved problems that still exist in coding theory. A well-established and highly relevant branch of mathematics, the theory of error-correcting codes is concerned with reliably transmitting data over a ‘noisy’ channel. Despite frequent use in a range of contexts, the subject still contains interesting unsolved problems that have resisted solution by some of the most prominent mathematicians of recent decades. Employing Sage—a free open-source mathematics software system—to illustrate ideas, this book is intended for graduate students and researchers in algebraic coding theory. The work may be used as supplementary reading material in a graduate course on coding theory or for self-study.
applied and computational harmonic analysis: Methods of Applied Mathematics with a MATLAB Overview Jon H. Davis, 2004 Broadly organized around the applications of Fourier analysis, Methods of Applied Mathematics with a MATLAB Overview covers both classical applications in partial differential equations and boundary value problems, as well as the concepts and methods associated to the Laplace, Fourier, and discrete transforms. Transform inversion problems are also examined, along with the necessary background in complex variables. A final chapter treats wavelets, short-time Fourier analysis, and geometrically-based transforms. The computer program MATLAB is emphasized throughout, and an introduction to MATLAB is provided in an appendix. Rich in examples, illustrations, and exercises of varying difficulty, this text can be used for a one- or two-semester course and is ideal for students in pure and applied mathematics, physics, and engineering.
applied and computational harmonic analysis: Engineering Applications of Noncommutative Harmonic Analysis Gregory S. Chirikjian, Alexander B. Kyatkin, 2000-09-28 The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is sti
applied and computational harmonic analysis: Issues in Computation: 2012 Edition , 2013-01-10 Issues in Computation / 2012 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Computational Chemistry. The editors have built Issues in Computation: 2012 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Computational Chemistry in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Computation: 2012 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
applied and computational harmonic analysis: Issues in Computation: 2011 Edition , 2012-01-09 Issues in Computation / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Computation. The editors have built Issues in Computation: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Computation in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Computation / 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
applied and computational harmonic analysis: The Bellman Function Technique in Harmonic Analysis Vasily Vasyunin, Alexander Volberg, 2020-08-06 A comprehensive reference on the Bellman function method and its applications to various topics in probability and harmonic analysis.
applied and computational harmonic analysis: Sparse Image and Signal Processing Jean-Luc Starck, Fionn Murtagh, Jalal Fadili, 2015-10-14 This thoroughly updated new edition presents state-of-the-art sparse and multiscale image and signal processing. It covers linear multiscale geometric transforms, such as wavelet, ridgelet, or curvelet transforms, and non-linear multiscale transforms based on the median and mathematical morphology operators. Along with an up-to-the-minute description of required computation, it covers the latest results in inverse problem solving and regularization, sparse signal decomposition, blind source separation, in-painting, and compressed sensing. New chapters and sections cover multiscale geometric transforms for three-dimensional data (data cubes), data on the sphere (geo-located data), dictionary learning, and nonnegative matrix factorization. The authors wed theory and practice in examining applications in areas such as astronomy, including recent results from the European Space Agency's Herschel mission, biology, fusion physics, cold dark matter simulation, medical MRI, digital media, and forensics. MATLAB® and IDL code, available online at www.SparseSignalRecipes.info, accompany these methods and all applications.
applied and computational harmonic analysis: Issues in Computation: 2013 Edition , 2013-05-01 Issues in Computation / 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Computing. The editors have built Issues in Computation: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Computing in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Computation / 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
applied and computational harmonic analysis: Signal Processing and Networking for Big Data Applications Zhu Han, Mingyi Hong, Dan Wang, 2017-04-27 This unique text helps make sense of big data in engineering applications using tools and techniques from signal processing. It presents fundamental signal processing theories and software implementations, reviews current research trends and challenges, and describes the techniques used for analysis, design and optimization. Readers will learn about key theoretical issues such as data modelling and representation, scalable and low-complexity information processing and optimization, tensor and sublinear algorithms, and deep learning and software architecture, and their application to a wide range of engineering scenarios. Applications discussed in detail include wireless networking, smart grid systems, and sensor networks and cloud computing. This is the ideal text for researchers and practising engineers wanting to solve practical problems involving large amounts of data, and for students looking to grasp the fundamentals of big data analytics.
applied and computational harmonic analysis: Compressive Sensing for Wireless Networks Zhu Han, Husheng Li, Wotao Yin, 2013-06-06 Compressive sensing is a new signal processing paradigm that aims to encode sparse signals by using far lower sampling rates than those in the traditional Nyquist approach. It helps acquire, store, fuse and process large data sets efficiently and accurately. This method, which links data acquisition, compression, dimensionality reduction and optimization, has attracted significant attention from researchers and engineers in various areas. This comprehensive reference develops a unified view on how to incorporate efficiently the idea of compressive sensing over assorted wireless network scenarios, interweaving concepts from signal processing, optimization, information theory, communications and networking to address the issues in question from an engineering perspective. It enables students, researchers and communications engineers to develop a working knowledge of compressive sensing, including background on the basics of compressive sensing theory, an understanding of its benefits and limitations, and the skills needed to take advantage of compressive sensing in wireless networks.
applied and computational harmonic analysis: Proceedings of the 12th European Conference on Information Warfare and Security Rauno Kuusisto, Erkki Kurkinen, 2013-11-07
applied and computational harmonic analysis: Numerical Fourier Analysis Gerlind Plonka, Daniel Potts, Gabriele Steidl, Manfred Tasche, 2019-02-05 This book offers a unified presentation of Fourier theory and corresponding algorithms emerging from new developments in function approximation using Fourier methods. It starts with a detailed discussion of classical Fourier theory to enable readers to grasp the construction and analysis of advanced fast Fourier algorithms introduced in the second part, such as nonequispaced and sparse FFTs in higher dimensions. Lastly, it contains a selection of numerical applications, including recent research results on nonlinear function approximation by exponential sums. The code of most of the presented algorithms is available in the authors’ public domain software packages. Students and researchers alike benefit from this unified presentation of Fourier theory and corresponding algorithms.
applied and computational harmonic analysis: A Mathematical Introduction to Compressive Sensing Simon Foucart, Holger Rauhut, 2013-08-13 At the intersection of mathematics, engineering, and computer science sits the thriving field of compressive sensing. Based on the premise that data acquisition and compression can be performed simultaneously, compressive sensing finds applications in imaging, signal processing, and many other domains. In the areas of applied mathematics, electrical engineering, and theoretical computer science, an explosion of research activity has already followed the theoretical results that highlighted the efficiency of the basic principles. The elegant ideas behind these principles are also of independent interest to pure mathematicians. A Mathematical Introduction to Compressive Sensing gives a detailed account of the core theory upon which the field is build. With only moderate prerequisites, it is an excellent textbook for graduate courses in mathematics, engineering, and computer science. It also serves as a reliable resource for practitioners and researchers in these disciplines who want to acquire a careful understanding of the subject. A Mathematical Introduction to Compressive Sensing uses a mathematical perspective to present the core of the theory underlying compressive sensing.
applied and computational harmonic analysis: Medical Image Computing and Computer-Assisted Intervention - MICCAI 2014 Polina Golland, Nobuhiko Hata, Christian Barillot, Joachim Hornegger, Robert Howe, 2014-08-31 The three-volume set LNCS 8673, 8674, and 8675 constitutes the refereed proceedings of the 17th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2014, held in Boston, MA, USA, in September 2014. Based on rigorous peer reviews, the program committee carefully selected 253 revised papers from 862 submissions for presentation in three volumes. The 53 papers included in the third volume have been organized in the following topical sections: shape and population analysis; brain; diffusion MRI; and machine learning.
applied and computational harmonic analysis: Landscapes of Time-Frequency Analysis Paolo Boggiatto, Elena Cordero, Maurice de Gosson, Hans G. Feichtinger, Fabio Nicola, Alessandro Oliaro, Anita Tabacco, 2019-01-30 The chapters in this volume are based on talks given at the inaugural Aspects of Time-Frequency Analysis conference held in Turin, Italy from July 5-7, 2017, which brought together experts in harmonic analysis and its applications. New connections between different but related areas were presented in the context of time-frequency analysis, encouraging future research and collaborations. Some of the topics covered include: Abstract harmonic analysis, Numerical harmonic analysis, Sampling theory, Compressed sensing, Mathematical signal processing, Pseudodifferential operators, and Applications of harmonic analysis to quantum mechanics. Landscapes of Time-Frequency Analysis will be of particular interest to researchers and advanced students working in time-frequency analysis and other related areas of harmonic analysis.
applied and computational harmonic analysis: Advances in Imaging and Electron Physics , 2014-03-11 Advances in Imaging & Electron Physics merges two long-running serials—Advances in Electronics & Electron Physics and Advances in Optical & Electron Microscopy. The series features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science and digital image processing, electromagnetic wave propagation, electron microscopy, and the computing methods used in all these domains. Contributions from leading authorities Informs and updates on all the latest developments in the field
applied and computational harmonic analysis: Morrey Spaces David Adams, 2015-12-31 In this set of lecture notes, the author includes some of the latest research on the theory of Morrey Spaces associated with Harmonic Analysis. There are three main claims concerning these spaces that are covered: determining the integrability classes of the trace of Riesz potentials of an arbitrary Morrey function; determining the dimensions of singular sets of weak solutions of PDE (e.g. The Meyers-Elcart System); and determining whether there are any “full” interpolation results for linear operators between Morrey spaces. This book will serve as a useful reference to graduate students and researchers interested in Potential Theory, Harmonic Analysis, PDE, and/or Morrey Space Theory.
applied and computational harmonic analysis: A Primer on Wavelets and Their Scientific Applications James S. Walker, 2008-01-29 In the first edition of his seminal introduction to wavelets, James S. Walker informed us that the potential applications for wavelets were virtually unlimited. Since that time thousands of published papers have proven him true, while also necessitating the creation of a new edition of his bestselling primer. Updated and fully revised to include th
applied and computational harmonic analysis: Sampling: Theory and Applications Stephen D. Casey, Kasso A. Okoudjou, Michael Robinson, Brian M. Sadler, 2020-05-20 The chapters of this volume are based on talks given at the eleventh international Sampling Theory and Applications conference held in 2015 at American University in Washington, D.C. The papers highlight state-of-the-art advances and trends in sampling theory and related areas of application, such as signal and image processing. Chapters have been written by prominent mathematicians, applied scientists, and engineers with an expertise in sampling theory. Claude Shannon’s 100th birthday is also celebrated, including an introductory essay that highlights Shannon’s profound influence on the field. The topics covered include both theory and applications, such as: • Compressed sensing• Non-uniform and wave sampling• A-to-D conversion• Finite rate of innovation• Time-frequency analysis• Operator theory• Mobile sampling issues Sampling: Theory and Applications is ideal for mathematicians, engineers, and applied scientists working in sampling theory or related areas.
applied and computational harmonic analysis: Shock capturing and high-order methods for hyperbolic conservation laws Jan Glaubitz , 2020-03-20 This thesis is concerned with the numerical treatment of hyperbolic conservation laws. These play an important role in describing many natural phenomena. Challenges in their theoretical as well as numerical study stem from the fact that spontaneous shock discontinuities can arise in their solutions, even in finite time and smooth initial states. Moreover, the numerical treatment of hyperbolic conservations laws involves many different fields from mathematics, physics, and computer science. As a consequence, this thesis also provides contributions to several different fields of research - which are still connected by numerical conservation laws, however. These contributions include, but are not limited to, the construction of stable high order quadrature rules for experimental data, the development of new stable numerical methods for conservation laws, and the investigation and design of shock capturing procedures as a means to stabilize high order numerical methods in the presence of (shock) discontinuities. Jan Glaubitz was born in Braunschweig, Germany, in 1990 and completed his mathematical studies (B.Sc., 2014, M.Sc., 2016, Dr. rer. nat., 2019) at TU Braunschweig. In 2016, he received awards from the German Mathematical Society (DMV) for his master's thesis as well as from the Society of Financial and Economic Mathematics of Braunschweig (VBFWM). In 2017, he was honored with the teaching award LehrLEO for the best tutorial at TU Braunschweig. Since 2020, he holds a position as a postdoctoral researcher at Dartmouth College, NH, USA.
applied and computational harmonic analysis: Harmonic Analysis And Wave Equations Jean-michel Coron, Tatsien Li, Wei-min Wang, 2019-08-19 This book is a collection of lecture notes for the LIASFMA School and Workshop on 'Harmonic Analysis and Wave Equations' which was held on May 8-18, 2017 at Fudan University, in Shanghai, China. The aim of the LIASFMA School and Workshop is to bring together Chinese and French experts to discuss and dissect recent progress in these related fields; and to disseminate state of art, new knowledge and new concepts, to graduate students and junior researchers.The book provides the readers with a unique and valuable opportunity to learn from and communicate with leading experts in nonlinear wave-type equations. The readers will witness the major development with the introduction of modern harmonic analysis and related techniques.
applied and computational harmonic analysis: High Performance Visualization E. Wes Bethel, Hank Childs, Charles Hansen, 2012-10-25 Visualization and analysis tools, techniques, and algorithms have undergone a rapid evolution in recent decades to accommodate explosive growth in data size and complexity and to exploit emerging multi- and many-core computational platforms. High Performance Visualization: Enabling Extreme-Scale Scientific Insight focuses on the subset of scientific visualization concerned with algorithm design, implementation, and optimization for use on today’s largest computational platforms. The book collects some of the most seminal work in the field, including algorithms and implementations running at the highest levels of concurrency and used by scientific researchers worldwide. After introducing the fundamental concepts of parallel visualization, the book explores approaches to accelerate visualization and analysis operations on high performance computing platforms. Looking to the future and anticipating changes to computational platforms in the transition from the petascale to exascale regime, it presents the main research challenges and describes several contemporary, high performance visualization implementations. Reflecting major concepts in high performance visualization, this book unifies a large and diverse body of computer science research, development, and practical applications. It describes the state of the art at the intersection of scientific visualization, large data, and high performance computing trends, giving readers the foundation to apply the concepts and carry out future research in this area.
applied and computational harmonic analysis: Convergence and Summability of Fourier Transforms and Hardy Spaces Ferenc Weisz, 2017-12-27 This book investigates the convergence and summability of both one-dimensional and multi-dimensional Fourier transforms, as well as the theory of Hardy spaces. To do so, it studies a general summability method known as theta-summation, which encompasses all the well-known summability methods, such as the Fejér, Riesz, Weierstrass, Abel, Picard, Bessel and Rogosinski summations. Following on the classic books by Bary (1964) and Zygmund (1968), this is the first book that considers strong summability introduced by current methodology. A further unique aspect is that the Lebesgue points are also studied in the theory of multi-dimensional summability. In addition to classical results, results from the past 20-30 years – normally only found in scattered research papers – are also gathered and discussed, offering readers a convenient “one-stop” source to support their work. As such, the book will be useful for researchers, graduate and postgraduate students alike.
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Applied and Computational Harmonic Analysis
Applied and Computational Harmonic Analysis (ACHA), for some in-depth study in this research direction. In this regard, function approximation on such data-deﬁned manifolds was also …

Applied and Computational Harmonic Analysis - Resear…
To reduce the computational cost, Qian introduced coordinate maximum [12, Deﬁnition 1] and proved that it is identical with the best n -tuple if the target function satisﬁes a certain …

Applied and Computational Harmonic Analysis
, to which the results of this paper can be applied. Indeed, the regularity of Lévy noises is the ﬁrst question to address in order to understand the regularity of sparse processes. Note that the …

Applied and Computational Harmonic Analysis - ronent…
Such manifold learning algorithms were initially applied to synthetic data sets, to illustrate their geo-metric properties and ﬂexibility [14,17]. More recently they have been applied to experimental as …

Applied and Computational Harmonic Analysis
Applied and Computational Harmonic Analysis (ACHA), for some in-depth study in this research direction. In this regard, function approximation on such data-deﬁned manifolds was also …

Applied and Computational Harmonic Analysis
Applied and Computational Harmonic Analysis ... IL 60637, United States America b Computational and Applied Mathematics Initiative, University of Chicago, IL 60637, United States …

The Lifting Scheme: A Custom-Design - CORE
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 3, 186 200 (1996) ARTICLE NO. 0015 The Lifting Scheme: A Custom-Design Construction of Biorthogonal Wavelets ... analysis …

Applied and Computational Harmonic Analysis - City U…
Y.-R. Li et al. / Appl. Comput. Harmon. Anal. 53 (2021) 332–348 333 where u denotes the unknown image to be recovered, K a blurring matrix, z an observed blurred image, and the …

Wavelets on the Interval and Fast Wavelet Transforms
Applied and Computational Harmonic Analysis, 1993, 10.1006/acha.1993.1005. hal-01311753 ... or image analysis (where the domain of interest is the Cartesian …

Applied and Computational Harmonic Analysis - City U…
Applied and Computational Harmonic Analysis. ... Sparsity within such representations, stemming from computational harmonic analysis, enables eﬃcient analysis and …

Stable super-resolution limit and smallest singular value …
W. Li, W. Liao / Appl. Comput. Harmon. Anal. 51 (2021) 118–156 119 an unknown discrete set Ω = {ω j}S j=1 in the periodic interval T =[0, 1). This collection of points sources

Applied and Computational Harmonic Analysis
article, we focus on the analysis of the spectra of. K. ρ,a. for 0 <ρ ≤. 1despite the fact that. K. ρ,a. with. ρ =1 does. not commute with such a simple 2nd order diﬀerential operator and that (3) is also …

Framelets: MRA-based constructions of wavelet fr…
Mar 12, 2001 · context is the decomposition operator (known also as the ‘analysis operator’) T∗:f→ f,g g∈X(Ψ). The system X(Ψ)is a Bessel system if the analysis operator is …

Applied and Computational Harmonic Analysis - Univer…
This paper develops a theory of harmonic analysis on spaces endowed with tree metrics, which are distances that arise naturally throughout pure and applied mathematics. We are …

Rescaled pure greedy algorithm for Hilbert and Ba…
JID:YACHA AID:1094 /COR [m3L; v1.162; Prn:3/11/2015; 15:07] P.1(1-15) Appl. Comput. Harmon. Anal. ••• (••••) •••–••• Contents lists ...

Math 994-002: Applied and Computational Harmonic A…
Math 994-002: Applied and Computational Harmonic Analysis, MSU, Spring 2020 Lecture 20: Time-Frequency Analysis of Stationary Processes March 26, 2020 Lecturer: Matthew Hirn …

Complex Wavelets for Shift Invariant Analysis and Filter…
the analysis and reconstruction ﬁlters have very similar frequency responses (i.e., are almost orthogonal, as is the case for the ﬁlters given later in Table 1), then it is an almost tight frame, which …

Applied and Computational Harmonic Analysis - City U…
Applied and Computational Harmonic Analysis. ... applied in various ﬁelds for more than a decade and there are some theoretical studies in the literature which provide good understanding of …

Math 994-002: Applied and Computational Harmonic A…
Mar 31, 2020 · Math 994-002: Applied and Computational Harmonic Analysis, MSU, Spring 2020 Lecture 21 & 22: Time-Frequency Analysis of fBm March 31, 2020 & April 2, 2020 Lecturer: …

Applied and Computational Harmonic Analysis - NSF P…
R. Vaughn, T. Berry and H. Antil Applied and Computational Harmonic Analysis 68 (2024) 101593 a collection of sample points, { } =1 ⊂ (M) ⊂ℝ which, together with equal weights, form a consistent …

Applied and Computational Harmonic Analysis - City U…
becomes the main factor of computational and storage eﬃciency for ﬁne approximation. Apart from the number of points of quadra- ture rules, another factor that incurs storage …

Solving Support Vector Machines in Reproducing K…
Preprint submitted to Applied and Computational Harmonic Analysis April 21, 2013. 1. Introduction The theory and practice of kernel-based methods is a fast growing research area. They have …

Applied and Computational Harmonic Analysis - EPFL
of continuous objects in sampling theory [2]. Initially deﬁned as piecewise-polynomial functions [3], they were further generalized, starting from their connection with diﬀerential operators …

Applied and Computational Harmonic Analysis
Applied and Computational Harmonic Analysis. ... in applications, as the dimension increases, it also makes computational cost skyrocket and the storage of frame coeﬃcients increase …

Applied and Computational Harmonic Analysis - weizm…
problem, see Beinert and Plonka [6]. From the computational aspect, as the classical phase problem is non-convex, the most commonly used phase-retrieval methods are iterative …

Applied and Computational Harmonic Analysis - NSF P…
Furthermore, we provide a weighted L2 convergence analysis of the ﬁnite volume scheme to the Fokker-Planck equation on N. The proposed ﬁnite volume scheme leads to a Markov …

Applied and Computational Harmonic Analysis - Zhou
Discrete Gabor analysis Orthonormal Gabor matrix Discrete time-frequency analysis We show that orthonormality of a discrete Gabor bases on Cn hinges heavily on the following pattern of its …

Applied and Computational Harmonic Analysis
In our theoretical analysis, we also improve the uniform recovery guarantee given in previous works [16,17]. Unlike previous results, our recovery guarantees are, up to log factors, …

Applied and Computational Harmonic Analysis - Resear…
Mar 3, 2014 · Applied and Computational Harmonic Analysis. ... optimization algorithms can be conveniently applied; see [2,12,33,39] for comprehensive overviews and the references therein.

Rigid-Motion Scattering for Texture Classiﬁcation
L. Sifre, S. Mallat / Applied and Computational Harmonic Analysis 00 (2014) 1–20 2 and rotations. We shall explain whyseparating both variables leads to importantloss of …

Theoretical Analysis of the Second-order Synchrosque…
Applied and Computational Harmonic Analysis, 2018, 45 (2), pp.379-404. ... Originally proposed as a post-processing method applied to the CWT, SST can alternatively be applied to …

Lecture 09: Windowed Fourier Ridges - Matthew Hi…
Math 994-002: Applied and Computational Harmonic Analysis, MSU, Spring 2020 Lecture 09: Windowed Fourier Ridges February 6, 2020 Lecturer: Matthew Hirn 4.3.2 Windowed Fourier …

MAT 271: Applied & Computational Harmonic A…
MAT 271: Applied & Computational Harmonic AnalysisHomework 1: due Monday, 04/24/23 Problem 1: Prove that the dilation operator: δs f (x) := 1 p s f ‡x s ·, s >0, is an isometry (i.e., norm …

Matthew J. Hirn - CV
Applied and Computational Harmonic Analysis, volume 36, number 1, pages 79–107, 2014. Code: Diffusion Maps for Changing Data. 6.Ronald R. Coifman and Matthew J. Hirn. Bi-stochastic …

Applied and Computational Harmonic Analysis - math.u…
Applied and Computational Harmonic Analysis. ... , Albert Fannjiang. b,∗. a. Applied Mathematics, National Chung Hsing University, Taichung 402, Taiwan. b. Department of Mathematics, …

Universality of deep convolutional neural networ…
Deep learning has been widely applied and brought breakthroughs in speech recognition, computer vision, and many other domains. Deep neural network architectures and computational …

CoSaMP: Iterative Signal Recovery From Incomplete …
The sampling matrix can be applied to a vector in time O(NlogN). The sampling matrix requires only O(mlogN) storage. Other types of sampling matrices, such as the random demodulator [35], enjoy …

City University of Hong Kong
Appl. Comput. Harmon. Anal. 60 (2022) 446–470 Contents lists available at ScienceDirect Applied and Computational Harmonic Analysis www.elsevier.com/locate/acha A ...

MAT 271: Applied & Computational Harmonic A…
MAT 271: Applied & Computational Harmonic AnalysisHomework 1: due Monday, 01/22/18 Problem 1: Prove that the dilation operator: –s f (x) :˘ 1 p s f ‡x s ·, s ¨0, is an isometry (i.e., norm …

Synchrosqueezed Wavelet Transforms: a Tool for Empi…
Program in Applied and Computational Mathematics Princeton University, 08544 ingrid@math.princeton.edu, jianfeng@math.princeton.edu, hauwu@math.princeton.edu ... can be …

MAT 280: Applied & Computational Harmonic A…
MAT 280: Applied & Computational Harmonic Analysis Supplementary Notes IV by Naoki Saito The Discrete Fourier Transform (DFT) The DFT can be viewed as either an approximation to the …

Shannon Sampling II. Connections to Learning Th…
Jul 22, 2004 · x3.Algorithm To allow noise, we make the following assumption. Special Assumption. The sampled values y = (yx)x2x have the form: For some f⁄ 2 H, and each x 2 x, …

Applied and Computational Harmonic Analysis
40,43]. That is, W is applied to each coil image independently. However, multiple coil images (or coil K-space data) in the pMRI system are correlated to each other since each coil image contains …

Applied and Computational Harmonic Analysis
required, i.e., the necessary number of computational steps increases. Since at present there exists a direct connection between the number of computational operations and the total energy …

Applied Harmonic Analysis, Massive Data Sets, Machin…
decades Applied Harmonic Analysis has been at the center of many signiﬁcant new ideas and methods crucial in a wide range of signal and image processing applications, and in the analysis and …

Theoretical analysis of the second-order ... - دانشیاری
Time-frequency analysis. Synchrosqueezing transform. Multicomponent signals. We consider in this article the analysis of multicomponent signals, deﬁned as …

Applied and Computational Harmonic Analysis - EPFL
of continuous objects in sampling theory [2]. Initially deﬁned as piecewise-polynomial functions [3], they were further generalized, starting from their connection with diﬀerential operators …

Applied and Computational Harmonic Analysis - fie.mu…
188 W. Qu et al. / Appl. Comput. Harmon. Anal. 55 (2021) 185–198 2. n-best approximation in the randomized unit disc In the beginning of this section we introduce the concept of random …

Math 994-002: Applied and Computational Harmonic A…
Math 994-002: Applied and Computational Harmonic Analysis, MSU, Spring 2020 Lecture 04: Uncertainty Principle and Introduction to DSP January 21, 2019 Lecturer: Matthew …

Neural collapse under cross-entropy loss - NSF Public A…
We simplify our analysis by dropping the bias. Another, more crucial, diﬀerence is that in actual deep learning, as considered in [12], the feature vectors u i are output by deep neural networks …

Applied And Computational Harmonic Analysis

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