Computational Radiology and Imaging

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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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.

• Approximation
• X-ray
• algorithms
• diagnostics
• differential equation
• electron microscopy
• imaging
• medical imaging
• medicine
• nuclear medicine
• optimization
• radiation
• radiology
• radiotherapy
• tomography

• Department of Mathematics, Tufts University, Medford, USA

  Christoph Börgers

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

  Frank Natterer

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