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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978-0-8218-0337-0 (9780821803370)
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An inversion formula for the horocyclic Radon transform on the real hyperbolic space by C. A. Berenstein and E. C. Tarabusi Image reconstruction and dense subspaces in the range of the Radon transform by W. K. Cheung and A. Markoe.On a spatial limited angle model for X-ray computerized tomography by A. Correa, R. Cruz, and P. M. Salzberg The backpropagation method in inverse acoustics by G. F. Crosta Some nonlinear aspects of the Radon transform by L. Ehrenpreis Spherical tomography and spherical integral geometry by S. Gindikin, J. Reeds, and L. Shepp That kappa operator: Gelfand-Graev-Shapiro inversion and Radon transforms on isotropic planes by E. L. Grinberg On uniqueness in the inverse conductivity problem with one boundary measurement by V. Isakov A method for finding discontinuities of functions from the tomographic data by A. I. Katsevich and A. G. Ramm Probability measure estimation using "weak" loss functions in positron emission tomography by A. Kuruc On stability estimates in the exterior problem for the Radon transform by S. Lissianoi Data correction and restoration in emission tomography by S. J. Lvin On problems of integral geometry in the non-convex domains by R. Mukhometov Recent developments in X-ray tomography by F. Natterer Some mathematical aspects of 3D X-ray tomography by V. P. Palamodov A note on consistency conditions in three dimensional diffuse tomography by S. K. Patch Radon transforms on curves in the plane by E. T. Quinto Inverse boundary value problems for first order perturbations of the Laplacian by G. Uhlmann Multidimensional analogue of the Erdelyi lemma and the Radon transform by A. I. Zaslavsky On the Willmore deficit of convex surfaces by J. Zhou.
