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Radon Transforms and Tomography
Edited by: Eric Todd Quinto, Tufts University, Medford, MA, Leon Ehrenpreis, Temple University, Philadelphia, PA, Adel Faridani, Oregon State University, Corvallis, OR, Fulton Gonzalez, Tufts University, Medford, MA, and Eric Grinberg, Temple University, Philadelphia, PA
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Contemporary Mathematics
2001; 261 pp; softcover
Volume: 278
ISBN-10: 0-8218-2135-0
ISBN-13: 978-0-8218-2135-0
List Price: US$80
Member Price: US$64
Order Code: CONM/278
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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.

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.

Table of Contents

Expository papers
  • C. A. Berenstein -- Local tomography and related problems
  • M. Cheney -- Tomography problems arising in synthetic aperture radar
  • A. Faridani, K. A. Buglione, P. Huabsomboon, O. D. Iancu, and J. McGrath -- Introduction to local tomography
  • F. Natterer -- Algorithms in ultrasound tomography
  • E. T. Quinto -- Radon transforms, differential equations, and microlocal analysis
  • L. Zalcman -- Supplementary bibliography to "A bibliographic survey of the Pompeiu problem"
Research papers
  • T. Bailey and M. Eastwood -- Twistor results for integral transforms
  • J. Boman -- Injectivity for a weighted vectorial Radon transform
  • O. Dorn, E. L. Miller, and C. M. Rappaport -- Shape reconstruction in 2D from limited-view multifrequency electromagnetic data
  • L. Ehrenpreis -- Three problems at Mount Holyoke
  • F. B. Gonzalez -- A Paley-Wiener theorem for central functions on compact Lie groups
  • I. Pesenson and E. L. Grinberg -- Inversion of the spherical Radon transform by a Poisson type formula
  • S. H. Izen and T. J. Bencic -- Application of the Radon transform to calibration of the NASA-Glenn icing research wind tunnel
  • A. Katsevich -- Range theorems for the Radon transform and its dual
  • S. K. Patch -- Moment conditions \(\emph{indirectly}\) improve image quality
  • A. Rieder -- Principles of reconstruction filter design in 2D-computerized tomography
  • B. Rubin and D. Ryabogin -- The \(k\)-dimensional Radon transform on the \(n\)-sphere and related wavelet transforms
  • S. Siltanen, J. L. Mueller, and D. Isaacson -- Reconstruction of high contrast 2-D conductivities by the algorithm of A. Nachman
  • L. B. Vertgeim -- Integral geometry problem with incomplete data for tensor fields in a complex space
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