Tomography, Impedance Imaging, and Integral Geometry

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Brand new. We distribute directly for the publisher. 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. Read more Show Less

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Overview

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.

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Editorial Reviews

Booknews
Twenty lectures from a seminar in South Hadley, Massachusetts, June 1993 report on the latest scientific advances regarding tomography and its application to medical and industrial imaging. The topics include image reconstruction and dense subspaces in the range of the radon transform, uniqueness in the inverse conductivity problem with one boundary measurement, and some mathematical aspects of 3D X-ray tomography. No index. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

Table of Contents

Preface
An inversion formula for the horocyclic Radon transform on the real hyperbolic space 1
Image reconstruction and dense subspaces in the range of the radon transform 7
On a spatial limited angle model for X-ray computerized tomography 25
The backpropagation method in inverse acoustics 35
Some nonlinear aspects of the radon transform 69
Spherical tomography and spherical integral geometry 83
That kappa operator: Gelfand-Graev-Shapiro inversion and radon transforms on isotropic planes 93
On uniqueness in the inverse conductivity problem with one boundary measurement 105
A method for finding discontinuities of functions from the tomographic data 115
Probability measure estimation using "weak" loss functions in positron emission tomography 125
On stability estimates in the exterior problem for the radon transform 143
Data correction and restoration in emission tomography 149
On problems of integral geometry in the non-convex domains 157
Recent developments in X-ray tomography 177
Some mathematical aspects of 3D X-ray tomography 199
A note on consistency conditions in three dimensional diffuse tomography 211
Radon transforms on curves in the plane 231
Inverse boundary value problems for first order perturbations of the Laplacian 245
Multidimensional analogue of the Erdelyi lemma and the radon transform 259
On the Willmore deficit of convex surfaces 279
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