The Radon Transform, Inverse Problems, and Tomography
About this Title
Gestur Ólafsson, Louisiana State University, Baton Rouge, LA and Eric Todd Quinto, Tufts University, Medford, MA, Editors
Publication: Proceedings of Symposia in Applied Mathematics
Publication Year 2006: Volume 63
ISBNs: 978-0-8218-3930-0 (print); 978-0-8218-9278-7 (online)
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 as metabolic 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 Inverse Problems 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 included references for further reading.
Graduate students and research mathematicians interested in inverse problems and mathematical tomography.
Table of Contents
- Eric Todd Quinto – An introduction to X-ray tomography and Radon transforms [MR 2208234]
- Alfred K. Louis – Development of algorithms in computerized tomography [MR 2208235]
- Adel Faridani – Fan-beam tomography and sampling theory [MR 2208236]
- Peter Kuchment – Generalized transforms of Radon type and their applications [MR 2208237]
- Peter Massopust – Inverse problems in pipeline inspection [MR 2208238]
- Liliana Borcea – Robust interferometric imaging in random media [MR 2208239]