Ebook: New Analytic and Geometric Methods in Inverse Problems: Lectures given at the EMS Summer School and Conference held in Edinburgh, Scotland 2000
Author: Yuri Burago David Shoenthal (auth.) Kenrick Bingham Yaroslav V. Kurylev Erkki Somersalo (eds.)
- Tags: Partial Differential Equations, Differential Geometry
- Year: 2004
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
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.
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.
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.
Content:
Front Matter....Pages I-XVI
Front Matter....Pages 1-1
Metric Geometry....Pages 3-50
Intertwining Operators in Inverse Scattering....Pages 51-92
Carleman Type Estimates and Their Applications....Pages 93-125
Gaussian Beams and Inverse Boundary Spectral Problems....Pages 127-163
Analytic Methods for Inverse Scattering Theory....Pages 165-185
Ray Transform on Riemannian Manifolds....Pages 187-259
On the Local Dirichlet-to-Neumann Map....Pages 261-279
Front Matter....Pages 281-281
Remarks on the Inverse Scattering Problem for Acoustic Waves....Pages 283-289
Asymptotic Properties of Solutions to 3-particle Schr?dinger Equations....Pages 291-307
Stability and Reconstruction in Gel’fand Inverse Boundary Spectral Problem....Pages 309-322
Uniqueness in Inverse Obstacle Scattering....Pages 323-336
Geometric Methods for Anisotopic Inverse Boundary Value Problems....Pages 337-351
Applications of the Oscillating-Decaying Solutions to Inverse Problems....Pages 353-365
Time-Dependent Methods in Inverse Scattering Theory....Pages 367-381
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.
Content:
Front Matter....Pages I-XVI
Front Matter....Pages 1-1
Metric Geometry....Pages 3-50
Intertwining Operators in Inverse Scattering....Pages 51-92
Carleman Type Estimates and Their Applications....Pages 93-125
Gaussian Beams and Inverse Boundary Spectral Problems....Pages 127-163
Analytic Methods for Inverse Scattering Theory....Pages 165-185
Ray Transform on Riemannian Manifolds....Pages 187-259
On the Local Dirichlet-to-Neumann Map....Pages 261-279
Front Matter....Pages 281-281
Remarks on the Inverse Scattering Problem for Acoustic Waves....Pages 283-289
Asymptotic Properties of Solutions to 3-particle Schr?dinger Equations....Pages 291-307
Stability and Reconstruction in Gel’fand Inverse Boundary Spectral Problem....Pages 309-322
Uniqueness in Inverse Obstacle Scattering....Pages 323-336
Geometric Methods for Anisotopic Inverse Boundary Value Problems....Pages 337-351
Applications of the Oscillating-Decaying Solutions to Inverse Problems....Pages 353-365
Time-Dependent Methods in Inverse Scattering Theory....Pages 367-381
....