Mathematics and Computer Science in Medical Imaging

1. Front Matter

   Pages I-VIII

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2. Introduction to and Overview of the Field

   1. Front Matter

      Pages 1-1

      PDF

   2. Introduction to Integral Transforms

      • Aldo Rescigno

      Pages 3-42

   3. Introduction to Discrete Reconstruction Methods in Medical Imaging

      • Max A. Viergever

      Pages 43-65

   4. Image Structure

      • Jan J. Koenderink

      Pages 67-104

   5. Fundamentals of the Radon Transform

      • Harrison H. Barrett

      Pages 105-125

   6. Regularization Techniques in Medical Imaging

      • Frank Natterer

      Pages 127-141

   7. Statistical Methods in Pattern Recognition

      • C. Robert Appledorn

      Pages 143-166

   8. Image Data Compression Techniques: A Survey

      • A. Todd-Pokropek

      Pages 167-195

   9. From 2D to 3D Representation

      • Gabor T. Herman

      Pages 197-220

   10. VLSI-Intensive Graphics Systems

       • Henry Fuchs

       Pages 221-240

   11. Knowledge Based Interpretation of Medical Images

       • John Fox, Nicholas Walker

       Pages 241-266

3. Selected Topics

   1. Front Matter

      Pages 267-267

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   2. Analytic Reconstruction Methods

      1. The Attenuated Radon Transform

         • Frank Natterer

         Pages 271-277

      2. Inverse Imaging with Strong Multiple Scattering

         • S. Leeman, V. C. Roberts, P. E. Chandler, L. A. Ferrari

         Pages 279-289

   3. Iterative Methods

      1. Possible Criteria for Choosing the Number of Iterations in Some Iterative Reconstruction Methods

         • M. Defrise

         Pages 293-303

      2. Initial Performance of Block-Iterative Reconstruction Algorithms

         • Gabor T. Herman, Haim Levkowitz

         Pages 305-317

      3. Maximum Likelihood Reconstruction in PET and TOFPET

         • Chin-Tu Chen, Charles E. Metz, Xiaoping Hu

         Pages 319-329

      4. Maximum Likelihood Reconstruction for SPECT Using Monte Carlo Simulation

         • Carey E. Floyd Jr., Stephen H. Manglos, Ronald J. Jaszczak, R. Edward Coleman

         Pages 331-338

      5. X-Ray Coded Source Tomosynthesis

         • I. E. Magnin

         Pages 339-349

Medical imaging is an important and rapidly expanding area in medical science. Many of the methods employed are essentially digital, for example computerized tomography, and the subject has become increasingly influenced by develop­ ments in both mathematics and computer science. The mathematical problems have been the concern of a relatively small group of scientists, consisting mainly of applied mathematicians and theoretical physicists. Their efforts have led to workable algorithms for most imaging modalities. However, neither the fundamentals, nor the limitations and disadvantages of these algorithms are known to a sufficient degree to the physicists, engineers and physicians trying to implement these methods. It seems both timely and important to try to bridge this gap. This book summarizes the proceedings of a NATO Advanced Study Institute, on these topics, that was held in the mountains of Tuscany for two weeks in the late summer of 1986. At another (quite different) earlier meeting on medical imaging, the authors noted that each of the speakers had given, there, a long introduction in their general area, stated that they did not have time to discuss the details of the new work, but proceeded to show lots of clinical results, while excluding any mathematics associated with the area.

• algorithms
• group
• imaging
• mathematics
• medical imaging
• complexity

• Department of Mathematics and Informatics, Delft University of Technology, Delft, The Netherlands

  Max A. Viergever

• Department of Medical Physics, University College London, London, UK

  Andrew Todd-Pokropek

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