Author: Eric Todd Quinto
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3111338010
Category : Mathematics
Languages : en
Pages : 252
Book Description
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.
Microlocal Analysis and Inverse Problems in Tomography and Geometry
Author: Eric Todd Quinto
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3111338010
Category : Mathematics
Languages : en
Pages : 252
Book Description
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.
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3111338010
Category : Mathematics
Languages : en
Pages : 252
Book Description
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.
Handbook of Mathematical Methods in Imaging
Author: Otmar Scherzer
Publisher: Springer Science & Business Media
ISBN: 0387929193
Category : Mathematics
Languages : en
Pages : 1626
Book Description
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.
Publisher: Springer Science & Business Media
ISBN: 0387929193
Category : Mathematics
Languages : en
Pages : 1626
Book Description
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 Radon Transform
Author: Sigurdur Helgason
Publisher: Springer Science & Business Media
ISBN: 9780817641092
Category : Mathematics
Languages : en
Pages : 214
Book Description
The Radon transform is an important topic in integral geometry which deals with the problem of expressing a function on a manifold in terms of its integrals over certain submanifolds. Solutions to such problems have a wide range of applications, namely to partial differential equations, group representations, X-ray technology, nuclear magnetic resonance scanning, and tomography. This second edition, significantly expanded and updated, presents new material taking into account some of the progress made in the field since 1980. Aimed at beginning graduate students, this monograph will be useful in the classroom or as a resource for self-study. Readers will find here an accessible introduction to Radon transform theory, an elegant topic in integral geometry.
Publisher: Springer Science & Business Media
ISBN: 9780817641092
Category : Mathematics
Languages : en
Pages : 214
Book Description
The Radon transform is an important topic in integral geometry which deals with the problem of expressing a function on a manifold in terms of its integrals over certain submanifolds. Solutions to such problems have a wide range of applications, namely to partial differential equations, group representations, X-ray technology, nuclear magnetic resonance scanning, and tomography. This second edition, significantly expanded and updated, presents new material taking into account some of the progress made in the field since 1980. Aimed at beginning graduate students, this monograph will be useful in the classroom or as a resource for self-study. Readers will find here an accessible introduction to Radon transform theory, an elegant topic in integral geometry.
Inside Out
Author: Gunther Uhlmann
Publisher: Cambridge University Press
ISBN: 9780521824699
Category : Mathematics
Languages : en
Pages : 424
Book Description
In this book, leading experts in the theoretical and applied aspects of inverse problems offer extended surveys on several important topics.
Publisher: Cambridge University Press
ISBN: 9780521824699
Category : Mathematics
Languages : en
Pages : 424
Book Description
In this book, leading experts in the theoretical and applied aspects of inverse problems offer extended surveys on several important topics.
The Radon Transform, Inverse Problems, and Tomography
Author: Gestur Ólafsson
Publisher: American Mathematical Soc.
ISBN: 0821839306
Category : Mathematics
Languages : en
Pages : 176
Book Description
Since their emergence in 1917, tomography and inverse problems remain active and important fields that combine pure and applied mathematics and provide strong interplay between diverse mathematical problems and applications. The applied side is best known for medical and scientific use, in particular, medical imaging, radiotherapy, and industrial non-destructive testing. Doctors use tomography to see the internal structure of the body or to find functional information, such asmetabolic processes, noninvasively. Scientists discover defects in objects, the topography of the ocean floor, and geological information using X-rays, geophysical measurements, sonar, or other data. This volume, based on the lectures in the Short Course The Radon Transform and Applications to InverseProblems at the American Mathematical Society meeting in Atlanta, GA, January 3-4, 2005, brings together articles on mathematical aspects of tomography and related inverse problems. The articles cover introductory material, theoretical problems, and practical issues in 3-D tomography, impedance imaging, local tomography, wavelet methods, regularization and approximate inverse, sampling, and emission tomography. All contributions are written for a general audience, and the authors have includedreferences for further reading.
Publisher: American Mathematical Soc.
ISBN: 0821839306
Category : Mathematics
Languages : en
Pages : 176
Book Description
Since their emergence in 1917, tomography and inverse problems remain active and important fields that combine pure and applied mathematics and provide strong interplay between diverse mathematical problems and applications. The applied side is best known for medical and scientific use, in particular, medical imaging, radiotherapy, and industrial non-destructive testing. Doctors use tomography to see the internal structure of the body or to find functional information, such asmetabolic processes, noninvasively. Scientists discover defects in objects, the topography of the ocean floor, and geological information using X-rays, geophysical measurements, sonar, or other data. This volume, based on the lectures in the Short Course The Radon Transform and Applications to InverseProblems at the American Mathematical Society meeting in Atlanta, GA, January 3-4, 2005, brings together articles on mathematical aspects of tomography and related inverse problems. The articles cover introductory material, theoretical problems, and practical issues in 3-D tomography, impedance imaging, local tomography, wavelet methods, regularization and approximate inverse, sampling, and emission tomography. All contributions are written for a general audience, and the authors have includedreferences for further reading.
Data-driven Models in Inverse Problems
Author: Tatiana A. Bubba
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3111251233
Category : Mathematics
Languages : en
Pages : 508
Book Description
Advances in learning-based methods are revolutionizing several fields in applied mathematics, including inverse problems, resulting in a major paradigm shift towards data-driven approaches. This volume, which is inspired by this cutting-edge area of research, brings together contributors from the inverse problem community and shows how to successfully combine model- and data-driven approaches to gain insight into practical and theoretical issues.
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3111251233
Category : Mathematics
Languages : en
Pages : 508
Book Description
Advances in learning-based methods are revolutionizing several fields in applied mathematics, including inverse problems, resulting in a major paradigm shift towards data-driven approaches. This volume, which is inspired by this cutting-edge area of research, brings together contributors from the inverse problem community and shows how to successfully combine model- and data-driven approaches to gain insight into practical and theoretical issues.
Semiclassical Analysis
Author: Maciej Zworski
Publisher: American Mathematical Soc.
ISBN: 0821883208
Category : Mathematics
Languages : en
Pages : 448
Book Description
"...A graduate level text introducing readers to semiclassical and microlocal methods in PDE." -- from xi.
Publisher: American Mathematical Soc.
ISBN: 0821883208
Category : Mathematics
Languages : en
Pages : 448
Book Description
"...A graduate level text introducing readers to semiclassical and microlocal methods in PDE." -- from xi.
Inverse Problems and Applications
Author: Gunther Uhlmann
Publisher: Cambridge University Press
ISBN: 1107032016
Category : Mathematics
Languages : en
Pages : 593
Book Description
Inverse problems lie at the heart of contemporary scientific inquiry and technological development. Applications include a variety of medical and other imaging techniques, which are used for early detection of cancer and pulmonary edema, location of oil and mineral deposits in the Earth's interior, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes, and modeling in the life sciences among others. The expository survey essays in this book describe recent developments in inverse problems and imaging, including hybrid or couple-physics methods arising in medical imaging, Calderon's problem and electrical impedance tomography, inverse problems arising in global seismology and oil exploration, inverse spectral problems, and the study of asymptotically hyperbolic spaces. It is suitable for graduate students and researchers interested in inverse problems and their applications.
Publisher: Cambridge University Press
ISBN: 1107032016
Category : Mathematics
Languages : en
Pages : 593
Book Description
Inverse problems lie at the heart of contemporary scientific inquiry and technological development. Applications include a variety of medical and other imaging techniques, which are used for early detection of cancer and pulmonary edema, location of oil and mineral deposits in the Earth's interior, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes, and modeling in the life sciences among others. The expository survey essays in this book describe recent developments in inverse problems and imaging, including hybrid or couple-physics methods arising in medical imaging, Calderon's problem and electrical impedance tomography, inverse problems arising in global seismology and oil exploration, inverse spectral problems, and the study of asymptotically hyperbolic spaces. It is suitable for graduate students and researchers interested in inverse problems and their applications.
Geometric Inverse Problems
Author: Gabriel P. Paternain
Publisher: Cambridge University Press
ISBN: 1316510875
Category : Mathematics
Languages : en
Pages : 369
Book Description
Cutting-edge mathematical tools are used in this treatment of recent developments in geometric inverse problems.
Publisher: Cambridge University Press
ISBN: 1316510875
Category : Mathematics
Languages : en
Pages : 369
Book Description
Cutting-edge mathematical tools are used in this treatment of recent developments in geometric inverse problems.
Reconstructive Integral Geometry
Author: Victor Palamodov
Publisher: Birkhäuser
ISBN: 3034879415
Category : Mathematics
Languages : en
Pages : 171
Book Description
This book covers facts and methods for the reconstruction of a function in a real affine or projective space from data of integrals, particularly over lines, planes, and spheres. Recent results stress explicit analytic methods. Coverage includes the relations between algebraic integral geometry and partial differential equations. The first half of the book includes the ray, the spherical mean transforms in the plane or in 3-space, and inversion from incomplete data.
Publisher: Birkhäuser
ISBN: 3034879415
Category : Mathematics
Languages : en
Pages : 171
Book Description
This book covers facts and methods for the reconstruction of a function in a real affine or projective space from data of integrals, particularly over lines, planes, and spheres. Recent results stress explicit analytic methods. Coverage includes the relations between algebraic integral geometry and partial differential equations. The first half of the book includes the ray, the spherical mean transforms in the plane or in 3-space, and inversion from incomplete data.