**Contemporary Mathematics**

Volume: 278;
2001;
261 pp;
Softcover

MSC: Primary 44; 92; 65; 35;
Secondary 43; 42; 30; 32

Print ISBN: 978-0-8218-2135-0

Product Code: CONM/278

List Price: $84.00

Individual Member Price: $67.20

**Electronic ISBN: 978-0-8218-7868-2
Product Code: CONM/278.E**

List Price: $84.00

Individual Member Price: $67.20

# Radon Transforms and Tomography

Share this page *Edited by *
*Eric Todd Quinto; Leon Ehrenpreis; Adel Faridani; Fulton Gonzalez; Eric Grinberg*

One of the most exciting features of the fields of Radon transforms and tomography is the strong relationship between high-level pure mathematics and applications to areas such as medical imaging and industrial nondestructive evaluation. The proceedings featured in this volume bring together fundamental research articles in the major areas of Radon transforms and tomography.

This volume includes expository papers that are of special interest to beginners as well as advanced researchers. Topics include local tomography and wavelets, Lambda tomography and related methods, tomographic methods in RADAR, ultrasound, Radon transforms and differential equations, and the Pompeiu problem.

The major themes in Radon transforms and tomography are represented among the research articles. Pure mathematical themes include vector tomography, microlocal analysis, twistor theory, Lie theory, wavelets, harmonic analysis, and distribution theory. The applied articles employ high-quality pure mathematics to solve important practical problems. Effective scanning geometries are developed and tested for a NASA wind tunnel. Algorithms for limited electromagnetic tomographic data and for impedance imaging are developed and tested. Range theorems are proposed to diagnose problems with tomography scanners. Principles are given for the design of X-ray tomography reconstruction algorithms, and numerical examples are provided.

This volume offers readers a comprehensive source of fundamental research useful to both beginners and advanced researchers in the fields.

#### Table of Contents

# Table of Contents

## Radon Transforms and Tomography

- Contents vii8 free
- Preface ix10 free
- I. Expository Papers 112 free
- Local tomography and related problems 314
- Tomography problems arising in synthetic aperture radar 1526
- Introduction to local tomography 2940
- Algorithms in ultrasound tomography 4960
- Radon transforms, differential equations, and microlocal analysis 5768
- Supplementary bibliography to "A bibliographic survey of the Pompeiu problem" 6980

- II. Research Papers 7586
- Twistor results for integral transforms 7788
- Injectivity for a weighted vectorial Radon transform 8798
- Shape reconstruction in 2d from limited-view multifrequency electromagnetic data 97108
- Three problems at Mount Holyoke 123134
- A Paley-Wiener theorem for central functions on compact Lie groups 131142
- Inversion of the spherical Radon transform by a Poisson type formula 137148
- Application of the Radon transform to calibration of the NASA-Glenn icing research wind tunnel 147158
- Range theorems for the Radon transform and its dual 167178
- Moment conditions indirectly improve image quality 193204
- Principles of reconstruction filter design in 2D-computerized tomography 207218
- The k-dimensional Radon transform on the n-sphere and related wavelet transforms 227238
- Reconstruction of high contrast 2-D conductivities by the algorithm of A. Nachman 241252
- Integral geometry problem with incomplete data for tensor fields in a complex space 255266

#### Readership

Graduate students and research mathematicians interested in integral transforms, harmonic analysis, numerical analysis, and partial differential equations, and in particular Radon transforms and tomography.