Mathematical Sciences: 1993 AMS-SIAM Summer Seminar: The Mathematics of Tomography, Impedance Imaging and Integral Geometry

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Computed tomography has grown from numerical analysis and algorithm development for planar X-ray tomography scanners to encompass a broad range of imaging techniques. Impedance imaging systems apply current to the surface of a body, measure the induced voltages on the surface, and from this information, reconstruct an approximation to the electrical conductivity and/or electrical permittivity in the interior. Mathematically, the problem is ill- posed and nonlinear, and a frequently used approximation reduces to a Radon transform. Integral geometry is the mathematical basis for tomography and one model for impedance imaging. The Radon transform on lines is the model of X-ray tomography and generalizations model emission tomography and problems in ultrasound. Tomographers use integral geometric theorems, such as inversion formulas and range characterizations, to create and improve reconstruction methods. This project will support the AMS-SIAM Summer Seminar in Applied Mathematics on the Mathematics of Tomography, Impedance Imaging, and Integral Geometry to be held June 7-18, 1993 at Mount Holyoke College in South Hadley, MA. One of the features of tomography is the strong relationship between high level mathematics (such as harmonic analysis, partial differential equations, microlocal analysis, and Lie group theory) and applications to medical imaging, impedance imaging, radiotherapy, and industrial non-destructive evaluation. The conference has the following main goals: (1) to give researchers in the field the opportunity to define and articulate the main problems of current interest and to isolate common themes and approaches and (2) to strengthen the connection between the pure and applied aspects of these areas and to facilitate dialogue between researchers in the various areas. Graduate students, recent doctoral recipients, and new researchers in the field will be encouraged to attend.