Mathematical Foundations of Imaging Tomography and Wavefield Inversion

Author: Anthony J. Devaney
Publisher: Cambridge University Press
ISBN: 1139510142
Format: PDF
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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.

Industrial Tomography

Author: Mi Wang
Publisher: Elsevier
ISBN: 1782421238
Format: PDF, ePub, Docs
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Industrial Tomography: Systems and Applications thoroughly explores the important tomographic techniques of industrial tomography, also discussing image reconstruction, systems, and applications. The text 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. Readers will find a comprehensive discussion on the ways tomography systems can be used to optimize the performance of a wide variety of industrial processes. Provides a comprehensive discussion on the different formats of tomography Includes an excellent overview of image reconstruction using a wide range of applications Presents a comprehensive discussion of tomography systems and their application in a wide variety of industrial processes

Handbook of Mathematical Methods in Imaging

Author: Otmar Scherzer
Publisher: Springer Science & Business Media
ISBN: 0387929193
Format: PDF, ePub
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The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

The Mathematics of Medical Imaging

Author: Timothy G. Feeman
Publisher: Springer
ISBN: 3319226657
Format: PDF, ePub
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The basic mathematics of computerized tomography, the CT scan, are aptly presented for an audience of undergraduates in mathematics and engineering. Assuming no prior background in advanced mathematical analysis, topics such as the Fourier transform, sampling, and discrete approximation algorithms are introduced from scratch and are developed within the context of medical imaging. A chapter on magnetic resonance imaging focuses on manipulation of the Bloch equation, the system of differential equations that is the foundation of this important technology. Extending the ideas of the acclaimed first edition, new material has been adeed to render an even more accessible textbook for course usage. This edition includes new discussions of the Radon transform, the Dirac delta function and its role in X-ray imaging, Kacmarz’s method and least squares approximation, spectral filtering, and more. Copious examples and exercises, new computer-based exercises, and additional graphics have been added to further delineate concepts. The use of technology has been revamped throughout with the incorporation of the open source programming environment R to illustrate examples and composition of graphics. All R code is available as extra source material on SpringerLink. From the reviews of the first edition: “This book is valuable, for it addresses with care and rigor the relevance of a variety of mathematical topics to a real-world problem. ...T his book is well written. It serves its purpose of focusing a variety of mathematical topics onto a real-world application that is in its essence mathematics.” –The Journal of Nuclear Medicine, Vol. 51 (12), December, 2010 “This new book by Timothy Feeman, truly intended to be a beginner’s guide, makes the subject accessible to undergraduates with a working knowledge of multivariable calculus and some experience with vectors and matrix methods. ...author handles the material with clarity and grace...” –The Mathematical Association of America, February, 2010

Inverse Theory and Applications in Geophysics

Author: Michael S. Zhdanov
Publisher: Elsevier
ISBN: 044462712X
Format: PDF, Mobi
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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.

Inverse Methods in Electromagnetic Imaging

Author: Wolfgang-M. Boerner
Publisher: Springer Science & Business Media
ISBN: 9400952716
Format: PDF, Kindle
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In recent years, there has been an increased interest in the use of polarization effects for radar and electromagnetic imaging problems (References 1, 2, and 3). The problem of electro magnetic imaging can be divided into the following areas: (1) Propagation of the Stokes' vector from the transmitter to the target region through various atmospheric conditions (rain, dust, fog, clouds, turbulence, etc.). (2) Scattering of the Stokes' vector from the object. (3) Scattering of the Stokes' vector from the rough surface, terrain, and the volume scattering. (4) Propagation of the Stokes' vector from the target region to the receiver. (5) The characteristics of the receiver relating the Stokes' vector to the output. The propagation characteristics of the Stokes' vector through various media can be described by the equation of transfer. Even though the scalar equation of transfer has been studied extensively in the past, the vector equation of transfer has not received as much attention. In recent years, however, a need for further study of the vector radiative transfer theory has become increasingly evident and several important studies have been reported. This paper presents a general formulation of the vector theory of radiative transfer under general anisotropic scattering conditions. Some useful solutions are also presented 4 8 for several practical situations. - 2. GENERAL FORMULATION OF VECTOR RADIATIVE TRANSFER THEORY Let us consider the plane-parallel problem Shovlll in Figure 1.

Full Seismic Waveform Modelling and Inversion

Author: Andreas Fichtner
Publisher: Springer Science & Business Media
ISBN: 9783642158070
Format: PDF
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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.

Transionospheric Synthetic Aperture Imaging

Author: Mikhail Gilman
Publisher: Birkhäuser
ISBN: 3319521276
Format: PDF
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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