Radon Transforms and Tomography

Radon Transforms and Tomography

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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.
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Product details

  • Paperback | 261 pages
  • 177.8 x 254 x 19.05mm | 453.59g
  • Providence, United States
  • English
  • 0821821350
  • 9780821821350

Table of contents

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