Inside out : inverse problems and applications

著者

書誌事項

Inside out : inverse problems and applications

edited by Gunther Uhlmann

（Mathematical Sciences Research Institute publications, 47, 60）

Cambridge University Press, c2003-2013

  • [v. 1] : hardback
  • v. 2 : hardback

タイトル別名

Inverse problems and applications

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注記

Spine title of v. 2: Inverse problems and applications

Includes bibliographical references

内容説明・目次

巻冊次

[v. 1] : hardback ISBN 9780521824699

内容説明

Inverse problems arise in practical situations such as medical imaging, geophysical exploration, and non-destructive evaluation where measurements made on the exterior of a body are used to determine properties of the inaccessible interior. There have been substantial developments in the mathematical theory of inverse problems, and applications have expanded greatly. In this volume, leading experts in the theoretical and applied aspects of inverse problems offer extended surveys on several important topics in modern inverse problems, such as microlocal analysis, reflection seismology, tomography, inverse scattering, and X-ray transforms. Each article covers a particular topic or topics with an emphasis on accessibility and integration with the whole volume. Thus the collection can be at the same time stimulating to researchers and accessible to graduate students.

目次

  • Preface
  • 1. Introduction to the mathematics of computed tomography Adel Faridani
  • 2. The attenuated X-ray transform: recent developments David V. Finch
  • 3. Inverse acoustic and electromagnetic scattering theory David Colton
  • 4. Inverse problems in transport theory Plamen Stefanov
  • 5. Near-field tomography P. Scott Carney and John C. Schotland
  • 6. Inverse problems for time harmonic electrodynamics Petri Ola, Lassi Paivarinta and Erkki Somersalo
  • 7. Microlocal analysis of the X-ray transform with sources on a curve David Finch, Ih-Ren Lan and Gunther Uhlmann
  • 8. Microlocal analysis of seismic inverse scattering Maarten V. de Hoop
  • 9. Sojourn times, singularities of the scattering kernel and inverse problems Vesselin Petkov and Luchezar Stoyanov
  • 10. Geometry and analysis in many-body scattering Andras Vasy
  • 11. A mathematical and deterministic analysis of the time-reversal mirror Claude Bardos.
巻冊次

v. 2 : hardback ISBN 9781107032019

内容説明

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.

目次

  • 1. The Calderon's inverse problem: imaging and invisibility Kari Astala, Matti Lassas and Lassi Paivarinta
  • 2. Resistor network approaches to electrical impedance tomography Liliana Borcea, Vladimir Druskin, Fernando Guevara Vasquez and Alexander V. Mamonov
  • 3. Calderon inverse problem in two dimensions Colin Guillarmou and Leo Tzou
  • 4. The Calderon problem on Riemannian manifolds Mikko Salo
  • 5. Enclosure methods for the Helmholtz-type equations Jenn-Nan Wang and Ting Zhou
  • 6. Multiwave methods via ultrasound Plamen Stefanov and Gunther Uhlmann
  • 7. Hybrid inverse problems and internal functionals Guillaume Bal
  • 8. Inverse problems for connections Gabriel P. Paternain
  • 9. Elastic-wave inverse scattering based on reverse time migration with active and passive source reflection data Valeriy Brytik, Maarten V. de Hoop and Robert D. van der Hilst
  • 10. Inverse problems in spectral geometry Kiril Datchev and Hamid Hezari
  • 11. Microlocal analysis of asymptotically hyperbolic spaces and high energy resolvent estimates Andras Vasy
  • 12. Transmission eigenvalues in inverse scattering theory Fioralba Cakoni and Houssem Haddar.

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