Advertisement
| mathematical foundations of imaging tomography and wavefield inversion: Mathematical Foundations of Imaging, Tomography and Wavefield Inversion Anthony J. Devaney, 2012-06-21 Inverse problems are of interest and importance across many branches of physics, mathematics, engineering and medical imaging. In this text, the foundations of imaging and wavefield inversion are presented in a clear and systematic way. The necessary theory is gradually developed throughout the book, progressing from simple wave equation based models to vector wave models. By combining theory with numerous MATLAB based examples, the author promotes a complete understanding of the material and establishes a basis for real world applications. Key topics of discussion include the derivation of solutions to the inhomogeneous and homogeneous Helmholtz equations using Green function techniques; the propagation and scattering of waves in homogeneous and inhomogeneous backgrounds; and the concept of field time reversal. Bridging the gap between mathematics and physics, this multidisciplinary book will appeal to graduate students and researchers alike. Additional resources including MATLAB codes and solutions are available online at www.cambridge.org/9780521119740. |
| mathematical foundations of imaging tomography and wavefield inversion: Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging Ke Chen, Carola-Bibiane Schönlieb, Xue-Cheng Tai, Laurent Younes, 2023-02-24 This handbook gathers together the state of the art on mathematical models and algorithms for imaging and vision. Its emphasis lies on rigorous mathematical methods, which represent the optimal solutions to a class of imaging and vision problems, and on effective algorithms, which are necessary for the methods to be translated to practical use in various applications. Viewing discrete images as data sampled from functional surfaces enables the use of advanced tools from calculus, functions and calculus of variations, and nonlinear optimization, and provides the basis of high-resolution imaging through geometry and variational models. Besides, optimization naturally connects traditional model-driven approaches to the emerging data-driven approaches of machine and deep learning. No other framework can provide comparable accuracy and precision to imaging and vision. Written by leading researchers in imaging and vision, the chapters in this handbook all start with gentle introductions, which make this work accessible to graduate students. For newcomers to the field, the book provides a comprehensive and fast-track introduction to the content, to save time and get on with tackling new and emerging challenges. For researchers, exposure to the state of the art of research works leads to an overall view of the entire field so as to guide new research directions and avoid pitfalls in moving the field forward and looking into the next decades of imaging and information services. This work can greatly benefit graduate students, researchers, and practitioners in imaging and vision; applied mathematicians; medical imagers; engineers; and computer scientists. |
| mathematical foundations of imaging tomography and wavefield inversion: Industrial Tomography Mi Wang, 2022-05-07 Industrial Tomography: Systems and Applications, Second Edition thoroughly explores the important techniques of industrial tomography, also discusses image reconstruction, systems, and applications. This book presents complex processes, including the way three-dimensional imaging is used to create multiple cross-sections, and how computer software helps monitor flows, filtering, mixing, drying processes, and chemical reactions inside vessels and pipelines. This book is suitable for materials scientists and engineers and applied physicists working in the photonics and optoelectronics industry or in the applications industries. - Provides a comprehensive discussion on the different formats of tomography, including advances in visualization and data fusion - Includes an excellent overview of image reconstruction using a wide range of applications - Presents a comprehensive discussion of tomography systems and their applications in a wide variety of industrial processes |
| mathematical foundations of imaging tomography and wavefield inversion: Bone Quantitative Ultrasound Pascal Laugier, Quentin Grimal, 2022-05-05 Many significant achievements in new ultrasound technologies to measure bone and models to elucidate the interaction and the propagation of ultrasonic waves in complex bone structures have been reported over the past ten years. Impaired bone remodeling affects not only the trabecular compartment but also the cortical one. Despite the crucial contribution of the cortical structure to the whole bone mechanical competence, cortical bone was understudied for a long time. A paradigm shift occurred around 2010, with a special focus placed on the importance of cortical bone. This has sparkled a great deal of interest in new ultrasound techniques to assess cortical bone. While our book ‘Bone Quantitative Ultrasound’ published in 2011 emphasized techniques to measure trabecular bone, this new book is devoted for a large part to the technologies introduced recently to measure cortical bone. These include resonant ultrasound spectroscopy, guided waves, scattering, and pulse-echo and tomography imaging techniques. Instrumentation, signal processing techniques and models used are detailed. Importantly, the data accumulated in recent years such as anisotropic stiffness, elastic engineering moduli, compression and shear wave speeds of cortical bones from various skeletal sites are presented comprehensively. A few chapters deal with the recent developments achieved in quantitative ultrasound of trabecular bone. These include (i) scattering-based approaches and their application to measure skeletal sites such as the spine and proximal femur and (ii) approaches exploiting the poro-elastic nature of bone. While bone fragility and osteoporosis are still the main motivation for developing bone QUS, this Book also includes chapters reporting ultrasound techniques developed for other applications of high interest such as 3-D imaging of the spine, assessment of implant stability and transcranial brain imaging. This book, together with the book ‘Bone Quantitative Ultrasound’ published in 2011 will provide a comprehensive overview of the methods and principles used in bone quantitative ultrasound and will be a benchmark for all novice or experienced researchers in the field. The book will offer recent experimental results and theoretical concepts developed so far and would be intended for researchers, graduate or undergraduate students, engineers, and clinicians who are involved in the field. The book should be considered as a complement to the first book publisher in 2011, rather than a second edition, in the sense that basic notions already presented in the first book are not repeated. |
| mathematical foundations of imaging tomography and wavefield inversion: Computational Methods for Electromagnetic Inverse Scattering Xudong Chen, 2018-03-07 A comprehensive and updated overview of the theory, algorithms and applications of for electromagnetic inverse scattering problems Offers the recent and most important advances in inverse scattering grounded in fundamental theory, algorithms and practical engineering applications Covers the latest, most relevant inverse scattering techniques like signal subspace methods, time reversal, linear sampling, qualitative methods, compressive sensing, and noniterative methods Emphasizes theory, mathematical derivation and physical insights of various inverse scattering problems Written by a leading expert in the field |
| mathematical foundations of imaging tomography and wavefield inversion: Fundamentals of Ultrasonic Phased Arrays Lester W. Schmerr Jr., 2014-08-13 This book describes in detail the physical and mathematical foundations of ultrasonic phased array measurements. The book uses linear systems theory to develop a comprehensive model of the signals and images that can be formed with phased arrays. Engineers working in the field of ultrasonic nondestructive evaluation (NDE) will find in this approach a wealth of information on how to design, optimize and interpret ultrasonic inspections with phased arrays. The fundamentals and models described in the book will also be of significant interest to other fields, including the medical ultrasound and seismology communities. A unique feature of this book is that it presents a unified theory of imaging with phased arrays that shows how common imaging methods such as the synthetic aperture focusing technique (SAFT), the total focusing method (TFM), and the physical optics far field inverse scattering (POFFIS) imaging method are all simplified versions of more fundamental and quantitative imaging approaches, called imaging measurement models. To enhance learning, this book first describes the fundamentals of phased array systems using 2-D models, so that the complex 3-D cases normally found in practice can be more easily understood. In addition to giving a detailed discussion of phased array systems, Fundamentals of Ultrasonic Phased Arrays also provides MATLAB® functions and scripts, allowing the reader to conduct simulations of ultrasonic phased array transducers and phased array systems with the latest modeling technology. |
| mathematical foundations of imaging tomography and wavefield inversion: Microwave Imaging Methods and Applications Matteo Pastorino, Andrea Randazzo, 2018-06-30 Microwave Imaging Methods and Applications provides practitioners and researchers with a complete overview of the latest and most important noninvasive and nondestructive techniques for inspecting structures and bodies by using microwaves. Placing emphasis on applications, the book considers many areas, from medical imaging and security… to industrial engineering and subsurface prospection. For each application, readers are presented with the objectives of the inspection and related challenges. Moreover, this groundbreaking resource details computational methods that can be used to solve inverse problems related to specific applications. Including clear examples or the most significant practical results, this forward-looking reference focuses on systems that have been recently developed. Professionals gain the knowledge needed to compare imaging methods used in different applications and develop new uses of imaging apparatuses and systems. |
| mathematical foundations of imaging tomography and wavefield inversion: A Data Engineering Approach to Wave Scattering Analysis with Applications in Radar, Sonar, Medical Diagnostics, Structural Flaw Detection and Intelligent Robotics Mark Hinders, 2025-01-02 Comprehensive resource exploring how recent advancements in computational capabilities open doors to new applications in wave scattering A Data Engineering Approach to Wave Scattering Analysis applies scattering analysis to many applications including radar, sonar, medical diagnosis, intelligent robotics, and more, enabling readers to implement new and better measurements with both novel instrumentation and artificial intelligence that automates the interpretation of various (and multiple) imaging data streams. Composed of 10 chapters, this book brings together separate scientific topics that share a common basis of knowledge and their unchanged mathematical techniques to ensure successful results. Through periodic exercises, this book reinforces the importance of revisiting derivations and reproducing established results. It also delves into the individuals who shaped scientific methods and technologies, exploring 81 notable names and providing insights into their professional journeys. Classic results from scattering are included in each chapter, and rather than simply pasting in plots from classic papers, these results have largely been reproduced for a more coherent reader experience. Written by an established academic in the field, A Data Engineering Approach to Wave Scattering Analysis includes information on various topics: Field equations, covering strain as a dimensionless measure of deformation, generalized Hooke's Law, and elastic and acoustic waves Reflection and refraction, covering reflection from a free surface and surface waves as well as the wave model of acoustic microscopy Guided waves, covering torsional modes, longitudinal waves, and flexural waves in rods, as well as data engineering for lamb wave tomography Inverse scattering, covering wavelet transforms and fingerprinting as well as applications of wavelet fingerprints such as roof fall detection A Data Engineering Approach to Wave Scattering is an essential up-to-date reference on the subject for researchers interested in radar, sonar, medical imaging, structural health monitoring, manufacturing process control, and autonomous vehicles, as well as upper-level undergraduates and graduate students in related programs of study. |
| mathematical foundations of imaging tomography and wavefield inversion: Radar Scattering and Imaging of Rough Surfaces Kun-Shan Chen, 2020-11-19 Radar scattering and imaging of rough surfaces is an active interdisciplinary area of research with many practical applications in fields such as mineral and resource exploration, ocean and physical oceanography, military and national defense, planetary exploration, city planning and land use, environmental science, and many more. By focusing on the most advanced analytical and numerical modeling and describing both forward and inverse modeling, Radar Scattering and Imaging of Rough Surfaces: Modeling and Applications with MATLAB® connects the scattering process to imaging techniques by vivid examples through numerical and experimental demonstrations and provides computer codes and practical uses. This book is unique in its simultaneous treatment of radar scattering and imaging. Key Features Bridges physical modeling with simulation for resolving radar imaging problems (the first comprehensive work to do so) Provides excellent basic and advanced information for microwave remote-sensing professionals in various fields of science and engineering Covers most advanced analytical and numerical modeling for both backscattering and bistatic scattering Includes MATLAB® codes useful not only for academics but also for radar engineers and scientists to develop tools applicable in different areas of earth studies Covering both the theoretical and the practical, Radar Scattering and Imaging of Rough Surfaces: Modeling and Applications with MATLAB® is an invaluable resource for professionals and students using remote sensing to study and explain the Earth and its processes. University and research institutes, electrical and radar engineers, remote-sensing image users, application software developers, students, and academics alike will benefit from this book. The author, Kun-Shan Chen, is an internationally known and respected engineer and scientist and an expert in the field of electromagnetic modeling. |
| mathematical foundations of imaging tomography and wavefield inversion: Transionospheric Synthetic Aperture Imaging Mikhail Gilman, Erick Smith, Semyon Tsynkov, 2017-04-13 This landmark monograph presents the most recent mathematical developments in the analysis of ionospheric distortions of SAR images and offers innovative new strategies for their mitigation. As a prerequisite to addressing these topics, the book also discusses the radar ambiguity theory as it applies to synthetic aperture imaging and the propagation of radio waves through the ionospheric plasma, including the anisotropic and turbulent cases. In addition, it covers a host of related subjects, such as the mathematical modeling of extended radar targets (as opposed to point-wise targets) and the scattering of radio waves off those targets, as well as the theoretical analysis of the start-stop approximation, which is used routinely in SAR signal processing but often without proper justification. The mathematics in this volume is clean and rigorous – no assumptions are hidden or ambiguously stated. The resulting work is truly interdisciplinary, providing both a comprehensive and thorough exposition of the field, as well as an accurate account of a range of relevant physical processes and phenomena. The book is intended for applied mathematicians interested in the area of radar imaging or, more generally, remote sensing, as well as physicists and electrical/electronic engineers who develop/operate spaceborne SAR sensors and perform the data processing. The methods in the book are also useful for researchers and practitioners working on other types of imaging. Moreover, the book is accessible to graduate students in applied mathematics, physics, engineering, and related disciplines. Praise for Transionospheric Synthetic Aperture Imaging: “I perceive that this text will mark a turning point in the field of synthetic aperture radar research and practice. I believe this text will instigate a new era of more rigorous image formation relieving the research, development and practitioner communities of inconsistent physical assumptions and numerical approaches.” – Richard Albanese, Senior Scientist, Albanese Defense and Energy Development LLC |
| mathematical foundations of imaging tomography and wavefield inversion: Mathematical Optics Vasudevan Lakshminarayanan, María L. Calvo, Tatiana Alieva, 2018-10-08 Going beyond standard introductory texts, Mathematical Optics: Classical, Quantum, and Computational Methods brings together many new mathematical techniques from optical science and engineering research. Profusely illustrated, the book makes the material accessible to students and newcomers to the field. Divided into six parts, the text presents state-of-the-art mathematical methods and applications in classical optics, quantum optics, and image processing. Part I describes the use of phase space concepts to characterize optical beams and the application of dynamic programming in optical waveguides. Part II explores solutions to paraxial, linear, and nonlinear wave equations. Part III discusses cutting-edge areas in transformation optics (such as invisibility cloaks) and computational plasmonics. Part IV uses Lorentz groups, dihedral group symmetry, Lie algebras, and Liouville space to analyze problems in polarization, ray optics, visual optics, and quantum optics. Part V examines the role of coherence functions in modern laser physics and explains how to apply quantum memory channel models in quantum computers. Part VI introduces super-resolution imaging and differential geometric methods in image processing. As numerical/symbolic computation is an important tool for solving numerous real-life problems in optical science, many chapters include Mathematica® code in their appendices. The software codes and notebooks as well as color versions of the book’s figures are available at www.crcpress.com. |
| mathematical foundations of imaging tomography and wavefield inversion: Electromagnetic Wave Propagation, Radiation, and Scattering Akira Ishimaru, 2017-09-05 One of the most methodical treatments of electromagnetic wave propagation, radiation, and scattering—including new applications and ideas Presented in two parts, this book takes an analytical approach on the subject and emphasizes new ideas and applications used today. Part one covers fundamentals of electromagnetic wave propagation, radiation, and scattering. It provides ample end-of-chapter problems and offers a 90-page solution manual to help readers check and comprehend their work. The second part of the book explores up-to-date applications of electromagnetic waves—including radiometry, geophysical remote sensing and imaging, and biomedical and signal processing applications. Written by a world renowned authority in the field of electromagnetic research, this new edition of Electromagnetic Wave Propagation, Radiation, and Scattering: From Fundamentals to Applications presents detailed applications with useful appendices, including mathematical formulas, Airy function, Abel’s equation, Hilbert transform, and Riemann surfaces. The book also features newly revised material that focuses on the following topics: Statistical wave theories—which have been extensively applied to topics such as geophysical remote sensing, bio-electromagnetics, bio-optics, and bio-ultrasound imaging Integration of several distinct yet related disciplines, such as statistical wave theories, communications, signal processing, and time reversal imaging New phenomena of multiple scattering, such as coherent scattering and memory effects Multiphysics applications that combine theories for different physical phenomena, such as seismic coda waves, stochastic wave theory, heat diffusion, and temperature rise in biological and other media Metamaterials and solitons in optical fibers, nonlinear phenomena, and porous media Primarily a textbook for graduate courses in electrical engineering, Electromagnetic Wave Propagation, Radiation, and Scattering is also ideal for graduate students in bioengineering, geophysics, ocean engineering, and geophysical remote sensing. The book is also a useful reference for engineers and scientists working in fields such as geophysical remote sensing, bio–medical engineering in optics and ultrasound, and new materials and integration with signal processing. |
| mathematical foundations of imaging tomography and wavefield inversion: The World of Applied Electromagnetics Akhlesh Lakhtakia, Cynthia M. Furse, 2017-08-08 This book commemorates four decades of research by Professor Magdy F. Iskander (Life Fellow IEEE) on materials and devices for the radiation, propagation, scattering, and applications of electromagnetic waves, chiefly in the MHz-THz frequency range as well on electromagnetics education. This synopsis of applied electromagnetics, stemming from the life and times of just one person, is meant to inspire junior researchers and reinvigorate mid-level researchers in the electromagnetics community. The authors of this book are internationally known researchers, including 14 IEEE fellows, who highlight interesting research and new directions in theoretical, experimental, and applied electromagnetics. |
| mathematical foundations of imaging tomography and wavefield inversion: Mathematical Modelling Hemen Dutta, 2023-06-12 This volume is a collection of chapters that present several key principles and theories, as well as their potential uses in the development of mathematical models in areas like waves, thermodynamic, electromagnetics, fluid dynamics, and catastrophes. The techniques and methodologies used in this book, on the other hand, should have a long-term impact and be applicable to a wide range of different topics of study and research. Each chapter should also help readers in gaining a better knowledge of the underlying and connected concepts. The companion volume (Contemporary Mathematics, Volume 787) is devoted to theory and application. |
| mathematical foundations of imaging tomography and wavefield inversion: Functional Analysis Joseph Muscat, 2014-07-23 This textbook is an introduction to functional analysis suited to final year undergraduates or beginning graduates. Its various applications of Hilbert spaces, including least squares approximation, inverse problems, and Tikhonov regularization, should appeal not only to mathematicians interested in applications, but also to researchers in related fields. Functional Analysis adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, based upon the classical sequence and function spaces and their operators. It assumes only a minimum of knowledge in elementary linear algebra and real analysis; the latter is redone in the light of metric spaces. It contains more than a thousand worked examples and exercises, which make up the main body of the book. |
| mathematical foundations of imaging tomography and wavefield inversion: Inverse Scattering Theory and Transmission Eigenvalues Fioralba Cakoni, David Colton, Houssem Haddar, 2022-12-07 Inverse scattering theory is a major theme in applied mathematics, with applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting challenges in the development of efficient inversion algorithms. A further complication is that anisotropic materials cannot be uniquely determined from given scattering data. In the first edition of Inverse Scattering Theory and Transmission Eigenvalues, the authors discussed methods for determining the support of inhomogeneous media from measured far field data and the role of transmission eigenvalue problems in the mathematical development of these methods. In this second edition, three new chapters describe recent developments in inverse scattering theory. In particular, the authors explore the use of modified background media in the nondestructive testing of materials and methods for determining the modified transmission eigenvalues that arise in such applications from measured far field data. They also examine nonscattering wave numbers—a subset of transmission eigenvalues—using techniques taken from the theory of free boundary value problems for elliptic partial differential equations and discuss the dualism of scattering poles and transmission eigenvalues that has led to new methods for the numerical computation of scattering poles. This book will be of interest to research mathematicians and engineers and physicists working on problems in target identification. It will also be useful to advanced graduate students in many areas of applied mathematics. |
| mathematical foundations of imaging tomography and wavefield inversion: Inverse Acoustic and Electromagnetic Scattering Theory David Colton, Rainer Kress, 2019-11-06 The inverse scattering problem is central to many areas of science and technology such as radar, sonar, medical imaging, geophysical exploration and nondestructive testing. This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. In this fourth edition, a number of significant additions have been made including a new chapter on transmission eigenvalues and a new section on the impedance boundary condition where particular attention has been made to the generalized impedance boundary condition and to nonlocal impedance boundary conditions. Brief discussions on the generalized linear sampling method, the method of recursive linearization, anisotropic media and the use of target signatures in inverse scattering theory have also been added. |
| mathematical foundations of imaging tomography and wavefield inversion: Signal and Image Processing for Remote Sensing C.H. Chen, 2024-06-11 Advances in signal and image processing for remote sensing have been tremendous in recent years. The progress has been particularly significant with the use of deep learning based techniques to solve remote sensing problems. These advancements are the focus of this third edition of Signal and Image Processing for Remote Sensing. It emphasizes the use of machine learning approaches for the extraction of remote sensing information. Other topics include change detection in remote sensing and compressed sensing. With 19 new chapters written by world leaders in the field, this book provides an authoritative examination and offers a unique point of view on signal and image processing. Features Includes all new content and does not replace the previous edition Covers machine learning approaches in both signal and image processing for remote sensing Studies deep learning methods for remote sensing information extraction that is found in other books Explains SAR, microwave, seismic, GPR, and hyperspectral sensors and all sensors considered Discusses improved pattern classification approaches and compressed sensing approaches Provides ample examples of each aspect of both signal and image processing This book is intended for university academics, researchers, postgraduate students, industry, and government professionals who use remote sensing and its applications. |
| mathematical foundations of imaging tomography and wavefield inversion: Electromagnetic and Optical Pulse Propagation Kurt E. Oughstun, 2019-07-17 This volume presents a detailed, rigorous treatment of the fundamental theory of electromagnetic pulse propagation in causally dispersive media that is applicable to dielectric, conducting, and semiconducting media. Asymptotic methods of approximation based upon saddle point methods are presented in detail. |
| mathematical foundations of imaging tomography and wavefield inversion: The Limits of Resolution Geoffrey de Villiers, E. Roy Pike, 2016-10-03 This beautiful book can be read as a novel presenting carefully our quest to get more and more information from our observations and measurements. Its authors are particularly good at relating it. --Pierre C. Sabatier This is a unique text - a labor of love pulling together for the first time the remarkably large array of mathematical and statistical techniques used for analysis of resolution in many systems of importance today – optical, acoustical, radar, etc.... I believe it will find widespread use and value. --Dr. Robert G.W. Brown, Chief Executive Officer, American Institute of Physics The mix of physics and mathematics is a unique feature of this book which can be basic not only for PhD students but also for researchers in the area of computational imaging. --Mario Bertero, Professor, University of Geneva a tour-de-force covering aspects of history, mathematical theory and practical applications. The authors provide a penetrating insight into the often confused topic of resolution and in doing offer a unifying approach to the subject that is applicable not only to traditional optical systems but also modern day, computer-based systems such as radar and RF communications. --Prof. Ian Proudler, Loughborough University a ‘must have’ for anyone interested in imaging and the spatial resolution of images. This book provides detailed and very readable account of resolution in imaging and organizes the recent history of the subject in excellent fashion.... I strongly recommend it. --Michael A.? Fiddy, Professor, University of North Carolina at Charlotte This book brings together the concept of resolution, which limits what we can determine about our physical world, with the theory of linear inverse problems, emphasizing practical applications. The book focuses on methods for solving illposed problems that do not have unique stable solutions. After introducing basic concepts, the contents address problems with continuous data in detail before turning to cases of discrete data sets. As one of the unifying principles of the text, the authors explain how non-uniqueness is a feature of measurement problems in science where precision and resolution is essentially always limited by some kind of noise. |
| mathematical foundations of imaging tomography and wavefield inversion: Acoustics of Fluid Media 1 Daniel Juvé, Marie-Annick Galland, Vincent Clair, 2024-11-13 Acoustics of Fluid Media 1 is intended for undergraduate students and engineering students, as well as graduate students and professionals in the industry who are increasingly faced with the need to consider acoustic constraints in the design of new products. The physical principles and theoretical foundations of acoustics in fluids are first developed, including reflection and refraction of plane and spherical waves. The book then introduces notions of signal processing applied to sound waves, followed by radiation from surface or volume acoustic sources and the use of Green’s functions, as well as the description of diffraction and scattering phenomena. The final chapters are devoted to sound propagation in ducts and room acoustics. Each chapter is accompanied by a limited number of exercises, ranging from the simple application of formulas to problems requiring a more advanced theoretical analysis or a numerical solution. Throughout the book, the theoretical results are illustrated with numerous figures obtained from measurements or numerical simulations resulting from the evaluation of complex formulas or from the use of a finite element solver. |
| mathematical foundations of imaging tomography and wavefield inversion: Microwave Imaging and Electromagnetic Inverse Scattering Problems Loreto Di Donato, Andrea F. Morabito, 2020-05-20 Microwave imaging techniques allow for the development of systems that are able to inspect, identify, and characterize in a noninvasive fashion under different scenarios, ranging from biomedical to subsurface diagnostics as well as from surveillance and security applications to nondestructive evaluation. Such great opportunities, though, are actually severely limited by difficulties arising from the solution of the underlying inverse scattering problem. As a result, ongoing research efforts in this area are devoted to developing inversion strategies and experimental apparatus so that they are as reliable and accurate as possible with respect to reconstruction capabilities and resolution performance, respectively. The intent of this Special Issue is to present the experiences of leading scientists in the electromagnetic inverse scattering community, as well as to serve as an assessment tool for people who are new to the area of microwave imaging and electromagnetic inverse scattering problems. |
| mathematical foundations of imaging tomography and wavefield inversion: Progress in Optics , 2013-08-08 In the 50 years since the first volume of Progress in Optics was published, optics has become one of the most dynamic fields of science. The volumes in this series that have appeared up to now contain more than 300 review articles by distinguished research workers, which have become permanent records for many important developments, helping optical scientists and optical engineers stay abreast of their fields. - Comprehensive, in-depth reviews - Edited by the leading authority in the field |
| mathematical foundations of imaging tomography and wavefield inversion: Archives of Acoustics Quarterly , 2018 |
| mathematical foundations of imaging tomography and wavefield inversion: Ondes acoustiques dans les fluides 1 Daniel Juvé, Marie-Annick Galland, Vincent Clair, 2025-05-21 Ondes acoustiques dans les fluides 1 s’adresse aux étudiants et élèves ingénieurs, ainsi qu’aux praticiens de l’industrie qui sont de plus en plus confrontés à la prise en compte de contraintes acoustiques lors de la conception de nouveaux produits. L’ouvrage rappelle les principes physiques et les fondements théoriques de l’acoustique dans les fluides, tout en introduisant des notions de traitement du signal appliquées aux ondes sonores. Il examine ensuite le rayonnement des sources acoustiques, qu’elles soient surfaciques ou volumiques, ainsi que l’utilisation des fonctions de Green et les phénomènes de diffraction par des obstacles. Enfin, il s’intéresse à la propagation du son dans les conduits et à l’acoustique des salles. Chaque chapitre est accompagné d’un nombre limité d’exercices, allant de la simple application de formules à des problèmes nécessitant une analyse théorique avancée ou une solution numérique. Les résultats théoriques sont illustrés par de nombreuses figures issues de mesures expérimentales, de l’évaluation numérique de formules complexes ou de l’utilisation d’un solveur par éléments finis. |
| mathematical foundations of imaging tomography and wavefield inversion: Seismic Inversion Gerard T. Schuster, 2017-07-01 This book describes the theory and practice of inverting seismic data for the subsurface rock properties of the earth. The primary application is for inverting reflection and/or transmission data from engineering or exploration surveys, but the methods described also can be used for earthquake studies. Seismic Inversion will be of benefit to scientists and advanced students in engineering, earth sciences, and physics. It is desirable that the reader has some familiarity with certain aspects of numerical computation, such as finite-difference solutions to partial differential equations, numerical linear algebra, and the basic physics of wave propagation. For those not familiar with the terminology and methods of seismic exploration, a brief introduction is provided. To truly understand the nuances of seismic inversion, we have to actively practice what we preach (or teach). Therefore, computational labs are provided for most of the chapters, and some field data labs are given as well. |
| mathematical foundations of imaging tomography and wavefield inversion: Geophysical Inversion J. Bee Bednar, 1992-01-01 This collection of papers on geophysical inversion contains research and survey articles on where the field has been and where it's going, and what is practical and what is not. Topics covered include seismic tomography, migration and inverse scattering. |
| mathematical foundations of imaging tomography and wavefield inversion: Inverse Problems in Wave Propagation Guy Chavent, George Papanicolaou, Paul Sacks, William Symes, 2012-12-06 Inverse problems in wave propagation concern extraction of information about distant structural features from the measurements of scattered waves. Tasks of this nature arise in geophysics, ocean acoustics, civil and environmental engineering, ultrasonic nondestructive testing, biomedical ultrasonics, radar, astrophysics, and other areas of science and technology. The papers in this volume represent most of these scientific and technical topics, together with fundamental mathematical investigations of the relation between waves and scatterers. |
| mathematical foundations of imaging tomography and wavefield inversion: Computer Vision for Visual Effects Richard J. Radke, 2012-11-19 Modern blockbuster movies seamlessly introduce impossible characters and action into real-world settings using digital visual effects. These effects are made possible by research from the field of computer vision, the study of how to automatically understand images. Computer Vision for Visual Effects will educate students, engineers and researchers about the fundamental computer vision principles and state-of-the-art algorithms used to create cutting-edge visual effects for movies and television. The author describes classical computer vision algorithms used on a regular basis in Hollywood (such as blue screen matting, structure from motion, optical flow and feature tracking) and exciting recent developments that form the basis for future effects (such as natural image matting, multi-image compositing, image retargeting and view synthesis). He also discusses the technologies behind motion capture and three-dimensional data acquisition. More than 200 original images demonstrating principles, algorithms and results, along with in-depth interviews with Hollywood visual effects artists, tie the mathematical concepts to real-world filmmaking. |
| mathematical foundations of imaging tomography and wavefield inversion: Full-3D Seismic Waveform Inversion Po Chen, En-Jui Lee, 2015-09-10 This book introduces a methodology for solving the seismic inverse problem using purely numerical solutions built on 3D wave equations and which is free of the approximations or simplifications that are common in classical seismic inversion methodologies and therefore applicable to arbitrary 3D geological media and seismic source models. Source codes provided allow readers to experiment with the calculations demonstrated and also explore their own applications. |
| mathematical foundations of imaging tomography and wavefield inversion: Full Seismic Waveform Modelling and Inversion Andreas Fichtner, 2010-11-16 Recent progress in numerical methods and computer science allows us today to simulate the propagation of seismic waves through realistically heterogeneous Earth models with unprecedented accuracy. Full waveform tomography is a tomographic technique that takes advantage of numerical solutions of the elastic wave equation. The accuracy of the numerical solutions and the exploitation of complete waveform information result in tomographic images that are both more realistic and better resolved. This book develops and describes state of the art methodologies covering all aspects of full waveform tomography including methods for the numerical solution of the elastic wave equation, the adjoint method, the design of objective functionals and optimisation schemes. It provides a variety of case studies on all scales from local to global based on a large number of examples involving real data. It is a comprehensive reference on full waveform tomography for advanced students, researchers and professionals. |
| mathematical foundations of imaging tomography and wavefield inversion: A Breviary of Seismic Tomography Guust Nolet, 2008-09-25 The first textbook to provide an extensive introduction to seismic tomography for advanced students and research practitioners. |
| mathematical foundations of imaging tomography and wavefield inversion: Time Series Analysis and Inverse Theory for Geophysicists David Gubbins, 2004-03-18 This unique textbook provides the foundation for understanding and applying techniques commonly used in geophysics to process and interpret modern digital data. The geophysicist's toolkit contains a range of techniques which may be divided into two main groups: processing, which concerns time series analysis and is used to separate the signal of interest from background noise; and inversion, which involves generating some map or physical model from the data. These two groups of techniques are normally taught separately, but are here presented together as parts I and II of the book. Part III describes some real applications and includes case studies in seismology, geomagnetism, and gravity. This textbook gives students and practitioners the theoretical background and practical experience, through case studies, computer examples and exercises, to understand and apply new processing methods to modern geophysical datasets. Solutions to the exercises are available on a website at http://publishing.cambridge.org/resources/0521819652 |
| mathematical foundations of imaging tomography and wavefield inversion: 3D Seismic Imaging Biondo Biondi, 2006 Accompanying CD-ROM includes PDF slides for teaching the material in the book and the C3-narrow-azimuth classic data set. |
| mathematical foundations of imaging tomography and wavefield inversion: Inverse Theory and Applications in Geophysics Michael S. Zhdanov, 2015-07-15 Geophysical Inverse Theory and Applications, Second Edition, brings together fundamental results developed by the Russian mathematical school in regularization theory and combines them with the related research in geophysical inversion carried out in the West. It presents a detailed exposition of the methods of regularized solution of inverse problems based on the ideas of Tikhonov regularization, and shows the different forms of their applications in both linear and nonlinear methods of geophysical inversion. It's the first book of its kind to treat many kinds of inversion and imaging techniques in a unified mathematical manner.The book is divided in five parts covering the foundations of the inversion theory and its applications to the solution of different geophysical inverse problems, including potential field, electromagnetic, and seismic methods. Unique in its focus on providing a link between the methods used in gravity, electromagnetic, and seismic imaging and inversion, it represents an exhaustive treatise on inversion theory.Written by one of the world's foremost experts, this work is widely recognized as the ultimate researcher's reference on geophysical inverse theory and its practical scientific applications. - Presents state-of-the-art geophysical inverse theory developed in modern mathematical terminology—the first to treat many kinds of inversion and imaging techniques in a unified mathematical way - Provides a critical link between the methods used in gravity, electromagnetic, and seismic imaging and inversion, and represents an exhaustive treatise on geophysical inversion theory - Features more than 300 illustrations, figures, charts and graphs to underscore key concepts - Reflects the latest developments in inversion theory and applications and captures the most significant changes in the field over the past decade |
| mathematical foundations of imaging tomography and wavefield inversion: Introduction to Microwave Imaging Natalia K. Nikolova, 2017-07-13 A one-stop tutorial for beginners covering the fundamentals of microwave imaging, including application examples and practical exercises. |
| mathematical foundations of imaging tomography and wavefield inversion: Seismic Ambient Noise Nori Nakata, Lucia Gualtieri, Andreas Fichtner, 2019-03-21 A comprehensive overview of seismic ambient noise, covering observations, physical origins, modelling, processing methods and applications in imaging and monitoring. |
| mathematical foundations of imaging tomography and wavefield inversion: Elements of 3D Seismology, third edition Christopher L. Liner, 2016-10-15 Elements of 3D Seismology, third edition is a thorough introduction to the acquisition, processing, and interpretation of 3D seismic data. This third edition is a major update of the second edition. Sections dealing with interpretation have been greatly revised in accordance with improved understanding and availability of data and software. Practice exercises have been added, as well as a 3D seismic survey predesign exercise. Discussions include: conceptual and historical foundations of modern reflection seismology; an overview of seismic wave phenomena in acoustic, elastic, and porous media; acquisition principles for land and marine seismic surveys; methods used to create 2D and 3D seismic images from field data; concepts of dip moveout, prestack migration, and depth migration; concepts and limitations of 3D seismic interpretation for structure, stratigraphy, and rock property estimation; and the interpretation role of attributes, impedance estimation, and AVO. This book is intended as a general text on reflection seismology, including wave propagation, data acquisition, processing, and interpretation and will be of interest to entry-level geophysicists, experts in related fields (geology, petroleum engineering), and experienced geophysicists in one subfield wishing to learn about another (e.g., interpreters wanting to learn about seismic waves or data acquisition). |
| mathematical foundations of imaging tomography and wavefield inversion: Transmission Electron Microscopy C. Barry Carter, David B. Williams, 2016-08-24 This text is a companion volume to Transmission Electron Microscopy: A Textbook for Materials Science by Williams and Carter. The aim is to extend the discussion of certain topics that are either rapidly changing at this time or that would benefit from more detailed discussion than space allowed in the primary text. World-renowned researchers have contributed chapters in their area of expertise, and the editors have carefully prepared these chapters to provide a uniform tone and treatment for this exciting material. The book features an unparalleled collection of color figures showcasing the quality and variety of chemical data that can be obtained from today’s instruments, as well as key pitfalls to avoid. As with the previous TEM text, each chapter contains two sets of questions, one for self assessment and a second more suitable for homework assignments. Throughout the book, the style follows that of Williams & Carter even when the subject matter becomes challenging—the aim is always to make the topic understandable by first-year graduate students and others who are working in the field of Materials Science Topics covered include sources, in-situ experiments, electron diffraction, Digital Micrograph, waves and holography, focal-series reconstruction and direct methods, STEM and tomography, energy-filtered TEM (EFTEM) imaging, and spectrum imaging. The range and depth of material makes this companion volume essential reading for the budding microscopist and a key reference for practicing researchers using these and related techniques. |
| mathematical foundations of imaging tomography and wavefield inversion: Principles of Computerized Tomographic Imaging Avinash C. Kak, Malcolm Slaney, 1988-01-01 Principles of Computerized Tomographic Imaging provides a comprehensive, tutorial-style introduction to the algorithms for reconstructing cross-sectional images from projection data and contains a complete overview of the engineering and signal processing algorithms necessary for tomographic imaging. In addition to the purely mathematical and algorithmic aspects of these algorithms, the book also discusses the artifacts caused by the nature of the various forms of energy sources that can be used for generating the projection data. Since the fundamental aspects of tomographic reconstruction algorithms have remained virtually the same since this book was originally published, it is just as useful today as it was in 1987. It explains, among other things, what happens when there is excessive noise in the projection data; when images are formed from insufficient projection data; and when refracting or diffracting energy sources are used for imaging. Audience: beginning graduate students or practitioners wishing to see the development of the algorithm from the ground up, as well as anyone interested in cross-sectional imaging for a wide variety of applications. |
Mathematics - Wikipedia
Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
Wolfram Mathematica: Modern Technical Computing
Mathematica is built to provide industrial-strength capabilities—with robust, efficient algorithms across all areas, capable of handling large-scale problems, with parallelism, GPU computing …
Mathematics | Definition, History, & Importance | Britannica
Apr 30, 2025 · mathematics, the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. It deals with …
Wolfram MathWorld: The Web's Most Extensive Mathematics …
May 22, 2025 · Comprehensive encyclopedia of mathematics with 13,000 detailed entries. Continually updated, extensively illustrated, and with interactive examples.
Wolfram|Alpha: Computational Intelligence
Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, …
MATHEMATICAL Definition & Meaning - Merriam-Webster
The meaning of MATHEMATICAL is of, relating to, or according with mathematics. How to use mathematical in a sentence.
Mathematics - Encyclopedia of Mathematics
Mar 30, 2012 · In the 17th century new questions in natural science and technology compelled mathematicians to concentrate their attention on the creation of methods to allow the …
MATHEMATICAL | English meaning - Cambridge Dictionary
mathematical formula The researchers used a mathematical formula to calculate the total population number. mathematical problem It was a mathematical problem that he could not …
Mathematical - definition of mathematical by The Free Dictionary
mathematical - of or pertaining to or of the nature of mathematics; "a mathematical textbook"; "slide rules and other mathematical instruments"; "a mathematical solution to a problem"; …
What is Mathematics? – Mathematical Association of America
Math is about getting the right answers, and we want kids to learn to think so they get the right answer. My reaction was visceral and immediate. “This is wrong. The emphasis needs to be on …
Mathematics - Wikipedia
Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
Wolfram Mathematica: Modern Technical Computing
Mathematica is built to provide industrial-strength capabilities—with robust, efficient algorithms across all areas, capable of handling large-scale problems, with parallelism, GPU computing and …
Mathematics | Definition, History, & Importance | Britannica
Apr 30, 2025 · mathematics, the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. It deals with …
Wolfram MathWorld: The Web's Most Extensive Mathematics …
May 22, 2025 · Comprehensive encyclopedia of mathematics with 13,000 detailed entries. Continually updated, extensively illustrated, and with interactive examples.
Wolfram|Alpha: Computational Intelligence
Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, …
MATHEMATICAL Definition & Meaning - Merriam-Webster
The meaning of MATHEMATICAL is of, relating to, or according with mathematics. How to use mathematical in a sentence.
Mathematics - Encyclopedia of Mathematics
Mar 30, 2012 · In the 17th century new questions in natural science and technology compelled mathematicians to concentrate their attention on the creation of methods to allow the …
MATHEMATICAL | English meaning - Cambridge Dictionary
mathematical formula The researchers used a mathematical formula to calculate the total population number. mathematical problem It was a mathematical problem that he could not …
Mathematical - definition of mathematical by The Free Dictionary
mathematical - of or pertaining to or of the nature of mathematics; "a mathematical textbook"; "slide rules and other mathematical instruments"; "a mathematical solution to a problem"; …
What is Mathematics? – Mathematical Association of America
Math is about getting the right answers, and we want kids to learn to think so they get the right answer. My reaction was visceral and immediate. “This is wrong. The emphasis needs to be on …
