Publisher Description

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. In the last twenty years or so there have been substantial developments in the mathematical theory of inverse problems, and applications have expanded greatly. In this book, 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.

Table of Contents

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.

Review

'It's a perfect introduction for students who want to learn the basic techniques with mathematical rigor and in a mathematical language ... the book is admirably clear and does a good job in motivating the reader ... It's safe to say that Uhlmann's book is a fingerpost in mathematical imaging for some time to come.' Bulletin of the American Mathematical Society 'This collection will undoubtedly be very useful both to the researchers in the field and postgraduate students.' European Mathematical Society Newsletter 'This collection will be undoubtedly very useful to the researchers in the filed and postgraduate students as well.' EMS Nerwsletter

Long Description

There have been substantial developments in the mathematical theory of inverse problems over the last twenty years and applications have expanded greatly in medical imaging, geophysical exploration, and non-destructive evaluation. In this book, leading experts in the theoretical and applied aspects of inverse problems offer extended surveys on several important topics in the field, such as microlocal analysis, reflection seismology, tomography, inverse scattering, and X-ray transforms.

Review Quote

'This collection will undoubtedly be very useful both to the researchers in the field and postgraduate students.' European Mathematical Society Newsletter

Promotional "Headline"

In this book, leading experts in the theoretical and applied aspects of inverse problems offer extended surveys on several important topics.

Description for Bookstore

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.

Description for Library

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.

Details