Radon Transforms and Tomography
About this Title
Eric Todd Quinto, Leon Ehrenpreis, Adel Faridani, Fulton Gonzalez and Eric Grinberg, Editors
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.
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
- Carlos A. Berenstein – Local tomography and related problems [MR 1851474]
- Margaret Cheney – Tomography problems arising in synthetic aperture radar [MR 1851475]
- Adel Faridani, Kory A. Buglione, Pallop Huabsomboon, Ovidiu D. Iancu and Jeanette McGrath – Introduction to local tomography [MR 1851476]
- Frank Natterer – Algorithms in ultrasound tomography [MR 1851477]
- Eric Todd Quinto – Radon transforms, differential equations, and microlocal analysis [MR 1851478]
- Lawrence Zalcman – Supplementary bibliography to: “A bibliographic survey of the Pompeiu problem” [in Approximation by solutions of partial differential equations (Hanstholm, 1991), 185–194, Kluwer Acad. Publ., Dordrecht, 1992; MR1168719 (93e:26001)] [MR 1851479]
- Toby Bailey and Michael Eastwood – Twistor results for integral transforms [MR 1851480]
- Jan Boman – Injectivity for a weighted vectorial Radon transform [MR 1851481]
- Oliver Dorn, Eric L. Miller and Carey M. Rappaport – Shape reconstruction in 2D from limited-view multifrequency electromagnetic data [MR 1851482]
- Leon Ehrenpreis – Three problems at Mount Holyoke [MR 1851483]
- Fulton B. Gonzalez – A Paley-Wiener theorem for central functions on compact Lie groups [MR 1851484]
- Isaac Pesenson and Eric L. Grinberg – Inversion of the spherical Radon transform by a Poisson type formula [MR 1851485]
- Steven H. Izen and Timothy J. Bencic – Application of the Radon transform to calibration of the NASA-Glenn Icing Research Wind Tunnel [MR 1851486]
- Alexander Katsevich – Range theorems for the Radon transform and its dual [MR 1851487]
- S. K. Patch – Moment conditions indirectly improve image quality [MR 1851488]
- Andreas Rieder – Principles of reconstruction filter design in 2D-computerized tomography [MR 1851489]
- Boris Rubin and Dmitry Ryabogin – The $k$-dimensional Radon transform on the $n$-sphere and related wavelet transforms [MR 1851490]
- Samuli Siltanen, Jennifer L. Mueller and David Isaacson – Reconstruction of high contrast 2-D conductivities by the algorithm of A. Nachman [MR 1851491]
- L. B. Vertgeim – Integral geometry problem with incomplete data for tensor fields in a complex space [MR 1851492]