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