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The articles collected in this volume are based on lectures given
at the IMA Workshop, "Computational Radiology and Imaging: Therapy
and Diagnostics," March 17-21, 1997. Introductory articles by the
editors have been added. The focus is on inverse problems involving
electromagnetic radiation and particle beams, with applications to
X-ray tomography, nuclear medicine, near-infrared imaging,
microwave imaging, electron microscopy, and radiation therapy
planning. Mathematical and computational tools and models which
play important roles in this volume include the X-ray transform and
other integral transforms, the linear Boltzmann equation and, for
near-infrared imaging, its diffusion approximation, iterative
methods for large linear and non-linear least-squares problems,
iterative methods for linear feasibility problems, and optimization
methods. The volume is intended not only for mathematical
scientists and engineers working on these and related problems, but
also for non-specialists. It contains much introductory expository
material, and a large number of references. Many unsolved
computational and mathematical problems of substantial practical
importance are pointed out.
G. T. Herman F. Natterer Universitat des Saarlandes Medical Image
Processing Group Department of Computer Science Angewandte
Mathematik und State University of New York at Informatik 66
Saarbrucken Buffalo Germany 4226 Ridge Lea Road Amherst, N. Y.
14226 USA In August 1978 we have attended a working conference on
Computer Aided Tomography and Ultrasonics in Medicine which was
held in Haifa, Israel under the auspices of the International
Federation for Information Pro- cessing [1]. That meeting, in
common with other meetings relating to computerized tomography,
concentrated on the physical, engineering and clinical aspects of
the topic, with little attention paid to the under- lying
mathematics, and no attention paid to recent developments in ma-
thematics inspired by computerized tomography (although not
necessarily) useful for computerized tomography). We both felt that
it would be worthwhile to organize a meeting of mathematicians
which would concen- trate on the mathematical aspects of
computerized tomography. This vol- ume (and the meeting on which it
is based) is the outcome of our decision in August 1978 to attempt
to bring together such a meeting. In the meantime much has been
published on the topic of computerized to- mography.
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