Geometric Inverse Problems
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Geometric Inverse Problems
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Author : Gabriel P. Paternain
language : en
Publisher: Cambridge University Press
Release Date : 2023-01-05
Geometric Inverse Problems written by Gabriel P. Paternain and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-05 with Mathematics categories.
This up-to-date treatment of recent developments in geometric inverse problems introduces graduate students and researchers to an exciting area of research. With an emphasis on the two-dimensional case, topics covered include geodesic X-ray transforms, boundary rigidity, tensor tomography, attenuated X-ray transforms and the Calderón problem. The presentation is self-contained and begins with the Radon transform and radial sound speeds as motivating examples. The required geometric background is developed in detail in the context of simple manifolds with boundary. An in-depth analysis of various geodesic X-ray transforms is carried out together with related uniqueness, stability, reconstruction and range characterization results. Highlights include a proof of boundary rigidity for simple surfaces as well as scattering rigidity for connections. The concluding chapter discusses current open problems and related topics. The numerous exercises and examples make this book an excellent self-study resource or text for a one-semester course or seminar.
Geometric Methods In Inverse Problems And Pde Control
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Author : Chrisopher B. Croke
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Methods In Inverse Problems And Pde Control written by Chrisopher B. Croke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This IMA Volume in Mathematics and its Applications GEOMETRIC METHODS IN INVERSE PROBLEMS AND PDE CONTROL contains a selection of articles presented at 2001 IMA Summer Program with the same title. We would like to thank Christopher B. Croke (University of Penn sylva nia), Irena Lasiecka (University of Virginia), Gunther Uhlmann (University of Washington), and Michael S. Vogelius (Rutgers University) for their ex cellent work as organizers of the two-week summer workshop and for editing the volume. We also take this opportunity to thank the National Science Founda tion for their support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA v PREFACE This volume contains a selected number of articles based on lectures delivered at the IMA 2001 Summer Program on "Geometric Methods in Inverse Problems and PDE Control. " The focus of this program was some common techniques used in the study of inverse coefficient problems and control problems for partial differential equations, with particular emphasis on their strong relation to fundamental problems of geometry. Inverse coef ficient problems for partial differential equations arise in many application areas, for instance in medical imaging, nondestructive testing, and geophys ical prospecting. Control problems involving partial differential equations may arise from the need to optimize a given performance criterion, e. g. , to dampen out undesirable vibrations of a structure , or more generally, to obtain a prescribed behaviour of the dynamics.
Spectral Geometry
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Author : Pierre H. Berard
language : en
Publisher: Springer
Release Date : 2006-11-14
Spectral Geometry written by Pierre H. Berard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Geometric Inverse Problems
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Author : Gabriel P. Paternain
language : en
Publisher: Cambridge University Press
Release Date : 2023-01-05
Geometric Inverse Problems written by Gabriel P. Paternain and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-05 with Mathematics categories.
Cutting-edge mathematical tools are used in this treatment of recent developments in geometric inverse problems.
New Analytic And Geometric Methods In Inverse Problems
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Author : Kenrick Bingham
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
New Analytic And Geometric Methods In Inverse Problems written by Kenrick Bingham and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
In inverse problems, the aim is to obtain, via a mathematical model, information on quantities that are not directly observable but rather depend on other observable quantities. Inverse problems are encountered in such diverse areas of application as medical imaging, remote sensing, material testing, geosciences and financing. It has become evident that new ideas coming from differential geometry and modern analysis are needed to tackle even some of the most classical inverse problems. This book contains a collection of presentations, written by leading specialists, aiming to give the reader up-to-date tools for understanding the current developments in the field.
Methods Of Inverse Problems In Physics
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Author : Dilip N. Ghosh Roy
language : en
Publisher: CRC Press
Release Date : 1991-03-14
Methods Of Inverse Problems In Physics written by Dilip N. Ghosh Roy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-03-14 with Science categories.
This interesting volume focuses on the second of the two broad categories into which problems of physical sciences fall-direct (or forward) and inverse (or backward) problems. It emphasizes one-dimensional problems because of their mathematical clarity. The unique feature of the monograph is its rigorous presentation of inverse problems (from quantum scattering to vibrational systems), transmission lines, and imaging sciences in a single volume. It includes exhaustive discussions on spectral function, inverse scattering integral equations of Gel'fand-Levitan and Marcenko, Povzner-Levitan and Levin transforms, Møller wave operators and Krein's functionals, S-matrix and scattering data, and inverse scattering transform for solving nonlinear evolution equations via inverse solving of a linear, isospectral Schrodinger equation and multisoliton solutions of the K-dV equation, which are of special interest to quantum physicists and mathematicians. The book also gives an exhaustive account of inverse problems in discrete systems, including inverting a Jacobi and a Toeplitz matrix, which can be applied to geophysics, electrical engineering, applied mechanics, and mathematics. A rigorous inverse problem for a continuous transmission line developed by Brown and Wilcox is included. The book concludes with inverse problems in integral geometry, specifically Radon's transform and its inversion, which is of particular interest to imaging scientists. This fascinating volume will interest anyone involved with quantum scattering, theoretical physics, linear and nonlinear optics, geosciences, mechanical, biomedical, and electrical engineering, and imaging research.
Diplomatische F Lschungen
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Author :
language : en
Publisher:
Release Date : 1988
Diplomatische F Lschungen written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.
Microlocal Analysis And Inverse Problems In Tomography And Geometry
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Author : Eric Todd Quinto
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-09-23
Microlocal Analysis And Inverse Problems In Tomography And Geometry written by Eric Todd Quinto and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-23 with Mathematics categories.
Microlocal Analysis has proven to be a powerful tool for analyzing and solving inverse problems; including answering questions about stability, uniqueness, recovery of singularities, etc. This volume, presents several studies on microlocal methods in problems in tomography, integral geometry, geodesic transforms, travel time tomography, thermoacoustic tomography, Compton CT, cosmology, nonlinear inverse problems, and others.
Linear And Nonlinear Inverse Problems With Practical Applications
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Author : Jennifer L. Mueller
language : en
Publisher: SIAM
Release Date : 2012-11-30
Linear And Nonlinear Inverse Problems With Practical Applications written by Jennifer L. Mueller and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-30 with Mathematics categories.
Inverse problems arise in practical applications whenever there is a need to interpret indirect measurements. This book explains how to identify ill-posed inverse problems arising in practice and gives a hands-on guide to designing computational solution methods for them, with related codes on an accompanying website. The guiding linear inversion examples are the problem of image deblurring, x-ray tomography, and backward parabolic problems, including heat transfer. A thorough treatment of electrical impedance tomography is used as the guiding nonlinear inversion example which combines the analytic-geometric research tradition and the regularization-based school of thought in a fruitful manner. This book is complete with exercises and project topics, making it ideal as a classroom textbook or self-study guide for graduate and advanced undergraduate students in mathematics, engineering or physics who wish to learn about computational inversion. It also acts as a useful guide for researchers who develop inversion techniques in high-tech industry.
Control Theory And Inverse Problems
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Author : Kaïs Ammari
language : en
Publisher: Springer Nature
Release Date : 2024-11-07
Control Theory And Inverse Problems written by Kaïs Ammari and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-07 with Science categories.
This volume presents a timely overview of control theory and inverse problems, and highlights recent advances in these active research areas. The chapters are based on talks given at the spring school "Control Theory & Inverse Problems” held in Monastir, Tunisia in May 2023. In addition to providing a snapshot of these two areas, chapters also highlight breakthroughs on more specific topics, such as: Control of hyperbolic systems The Helffer-Nier Conjecture Rapid stabilization of the discretized Vlasov system Exponential stability of a delayed thermoelastic system Control Theory and Inverse Problems will be a valuable resource for both established researchers as well as more junior members of the community.