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Computational Radiology and Imaging

Therapy and Diagnostics

  • Book
  • © 1999

Overview

Editors:
  1. Christoph Börgers

    1. Department of Mathematics, Tufts University, Medford, USA

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  2. Frank Natterer

    1. Institut für Numerische und instrumentelle Mathematik, Universität Münster, Münster, Germany

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 110)

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About this book

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.

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    1. The Radiation Therapy Planning Problem

      • Christoph Börgers
      Pages 1-16

    2. Mathematical Models for Medical Imaging

      • Frank Natterer
      Pages 17-32

  3. Articles by Workshop Speakers

    1. Tomography Through the Transport Equation

      • D. S. Anikonov, A. E. Kovtanyuk, I. V. Prokhorov
      Pages 33-44

    2. A General Framework for Iterative Reconstruction Algorithms in Optical Tomography, Using a Finite Element Method

      • Simon R. Arridge, Martin Schweiger
      Pages 45-70

    3. Scattered Radiation in Nuclear Medicine: A Case Study on the Boltzmann Transport Equation

      • Harrison H. Barrett, Brandon Gallas, Eric Clarkson, Anne Clough
      Pages 71-100

    4. Mathematical Aspects of Radiation Therapy Treatment Planning: Continuous Inversion Versus Full Discretization and Optimization Versus Feasibility

      • Yair Censor
      Pages 101-112

    5. Early Results on General Vertex Sets and Truncated Projections in Cone-Beam Tomography

      • Rolf Clackdoyle, Michel Defrise, Frédéric Noo
      Pages 113-135

    6. Mathematical Problems in Microwave Medical Imaging

      • David Colton, Peter Monk
      Pages 137-156

    7. Image Reconstruction from Experimental Data in Diffusion Tomography

      • Michael V. Klibanov, Thomas R. Lucas, Robert M. Frank
      Pages 157-181

    8. The Application of the X-ray Transform to 3D Conformal Radiotherapy

      • Robert Y. Levine, Eugene A. Gregerson, Marcia M. Urie
      Pages 183-227

    9. Optimization Methods for Radiation Therapy Plans

      • Weldon A. Lodwick, Steve McCourt, Francis Newman, Stephen Humphries
      Pages 229-249

    10. Fully Three-Dimensional Reconstruction in Electron Microscopy

      • Roberto Marabini, Gabor T. Herman, José M. Carazo
      Pages 251-281

  4. Back Matter

    Pages 282-288
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Editors and Affiliations

  • Department of Mathematics, Tufts University, Medford, USA

    Christoph Börgers

  • Institut für Numerische und instrumentelle Mathematik, Universität Münster, Münster, Germany

    Frank Natterer

Bibliographic Information

  • Book Title: Computational Radiology and Imaging

  • Book Subtitle: Therapy and Diagnostics

  • Editors: Christoph Börgers, Frank Natterer

  • Series Title: The IMA Volumes in Mathematics and its Applications

  • DOI: https://doi.org/10.1007/978-1-4612-1550-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1999

  • Hardcover ISBN: 978-0-387-98799-6Published: 23 April 1999

  • Softcover ISBN: 978-1-4612-7189-5Published: 23 October 2012

  • eBook ISBN: 978-1-4612-1550-9Published: 06 December 2012

  • Series ISSN: 0940-6573

  • Series E-ISSN: 2198-3224

  • Edition Number: 1

  • Number of Pages: X, 288

  • Topics: Physiological, Cellular and Medical Topics, Analysis

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