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Tomography, Impedance Imaging, and Integral Geometry
Edited by: Eric Todd Quinto, Margaret Cheney, and Peter Kuchment

Lectures in Applied Mathematics
1994; 287 pp; softcover
Volume: 30
ISBN-10: 0-8218-0337-9
ISBN-13: 978-0-8218-0337-0
List Price: US$67
Member Price: US$53.60
Order Code: LAM/30
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One of the most exciting features of tomography is the strong relationship between high-level 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 AMS-SIAM 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.


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 X-ray 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: Gelfand-Graev-Shapiro 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 non-convex domains
  • F. Natterer -- Recent developments in X-ray tomography
  • V. P. Palamodov -- Some mathematical aspects of 3D X-ray 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
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