Lectures in Applied Mathematics 1994; 287 pp; softcover Volume: 30 ISBN10: 0821803379 ISBN13: 9780821803370 List Price: US$63 Member Price: US$50.40 Order Code: LAM/30
 One of the most exciting features of tomography is the strong relationship between highlevel pure mathematics (such as harmonic analysis, partial differential equations, microlocal analysis, and group theory) and applications to medical imaging, impedance imaging, radiotherapy, and industrial nondestructive evaluation. This book contains the refereed proceedings of the AMSSIAM Summer Seminar on Tomography, Impedance Imaging, and Integral Geometry, held at Mount Holyoke College in June 1993. A number of common themes are found among the papers. Group theory is fundamental both to tomographic sampling theorems and to pure Radon transforms. Microlocal and Fourier analysis are important for research in all three fields. Differential equations and integral geometric techniques are useful in impedance imaging. In short, a common body of mathematics can be used to solve dramatically different problems in pure and applied mathematics. Radon transforms can be used to model impedance imaging problems. These proceedings include exciting results in all three fields represented at the conference. Readership Research mathematicians. Table of Contents  C. A. Berenstein and E. C. Tarabusi  An inversion formula for the horocyclic Radon transform on the real hyperbolic space
 W. K. Cheung and A. Markoe  Image reconstruction and dense subspaces in the range of the Radon transform
 A. Correa, R. Cruz, and P. M. Salzberg  On a spatial limited angle model for Xray computerized tomography
 G. F. Crosta  The backpropagation method in inverse acoustics
 L. Ehrenpreis  Some nonlinear aspects of the Radon transform
 S. Gindikin, J. Reeds, and L. Shepp  Spherical tomography and spherical integral geometry
 E. L. Grinberg  That kappa operator: GelfandGraevShapiro inversion and Radon transforms on isotropic planes
 V. Isakov  On uniqueness in the inverse conductivity problem with one boundary measurement
 A. I. Katsevich and A. G. Ramm  A method for finding discontinuities of functions from the tomographic data
 A. Kuruc  Probability measure estimation using "weak" loss functions in positron emission tomography
 S. Lissianoi  On stability estimates in the exterior problem for the Radon transform
 S. J. Lvin  Data correction and restoration in emission tomography
 R. Mukhometov  On problems of integral geometry in the nonconvex domains
 F. Natterer  Recent developments in Xray tomography
 V. P. Palamodov  Some mathematical aspects of 3D Xray tomography
 S. K. Patch  A note on consistency conditions in three dimensional diffuse tomography
 E. T. Quinto  Radon transforms on curves in the plane
 G. Uhlmann  Inverse boundary value problems for first order perturbations of the Laplacian
 A. I. Zaslavsky  Multidimensional analogue of the Erdelyi lemma and the Radon transform
 J. Zhou  On the Willmore deficit of convex surfaces
