# Integral Geometry and Tomography

Share this page *Edited by *
*E. Grinberg; E. Todd Quinto*

This book contains the proceedings of an AMS-IMS-SIAM Joint Summer Research
Conference on Integral Geometry and Tomography, held in June 1989 at Humboldt
State University in Arcata, California. The papers collected here represent
current research in these two interrelated fields. The articles in pure
mathematics range over such diverse areas as combinatorics, geometric
inequalities, micro-local analysis, group theory, and harmonic analysis. The
interplay between Lie group theory, geometry, harmonic analysis, and Radon
transforms is well covered. The papers on tomography reflect current research
on X-ray computed tomography, as well as radiation dose planning, radar, and
partial differential equations.

In addition to describing current research, this book provides a useful
perspective on the interplay between the fields. For example, abstract
theorems about Radon transforms are used to understand applied mathematics,
while applied mathematics motivates some of the results in pure mathematics.
Though directed at specialists in the field, the book would also be of interest
to others who wish to understand current research in these areas and to witness
how they relate to other branches of mathematics.

# Table of Contents

## Integral Geometry and Tomography

- Contents ix10 free
- Preface xi12 free
- Admissible complexes for the combinatorial radon transform. A Progress Report 114 free
- On generalized radon transforms with unknown measures 518
- Paley-Wiener theorems on rank one symmetric spaces of noncompact type 1730
- Inversion of the X-ray transform: continuous vs. discrete 3144
- The mathematics and physics of radiation dose planning using X-rays 4154
- The radon transform and tensor products 5770
- An application of a multidimensional sampling theorem to computed tomography 6578
- The radon transform for symmetric forms on real projective spaces 8194
- Bi-invariant differential operators on the complex motion group and therange of the d-plane transform on Cn 97110
- Processes of flats induced by higher-dimensional processes II 111124
- Microlocal techniques in integral geometry 121134
- Backscattering comes to the rescue 137150
- The totally-geodesic radon transform on constant curvature spaces 141154
- An application for a limited solid angle X-ray transform 151164
- On a conjectured projection inequality of Petty 171186
- A generalized radon transform in wideband radar 183198
- Summability and approximate reconstruction from radon transform data 189204
- An inverse problem for a transport equation and integral geometry 221236
- Invariant radon transforms on a symmetric space 233248
- Nonuniqueness and the null space of the divergent beam X-ray transform 243258