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Mathematical Methods in Tomography

Proceedings of a Conference held in Oberwolfach, Germany, 5-11 June, 1990

  • Conference proceedings
  • © 1991

Overview

Editors:
  1. Gabor T. Herman

    1. Department of Radiology, University of Pennsylvania, Philadelphia, USA

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  2. Alfred K. Louis

    1. Fachbereich Mathematik, Universität des Saarlandes, Saarbrücken, Germany

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    You can also search for this editor in PubMed   Google Scholar

  3. Frank Natterer

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

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1497)

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Table of contents (21 papers)

  1. Front Matter

    Pages I-X
    Download chapter PDF

  2. Helgason's support theorem for Radon transforms — A new proof and a generalization

    • Jan Boman
    Pages 1-5

  3. Singular value decompositions for Radon transforms

    • Peter Maass
    Pages 6-14

  4. Image reconstruction in Hilbert space

    • W. R. Madych
    Pages 15-45

  5. A problem of integral geometry for a family of rays with multiple reflections

    • R. G. Mukhometov
    Pages 46-52

  6. Inversion formulas for the three-dimensional ray transform

    • Victor P. Palamodov
    Pages 53-62

  7. Backscattered photons — Are they useful for a surface-near tomography?

    • Volkmar Friedrich
    Pages 63-65

  8. Mathematical framework of cone beam 3D reconstruction via the first derivative of the radon transform

    • Pierre Grangeat
    Pages 66-97

  9. Diffraction tomography some applications and extension to 3-D ultrasound imaging

    • Patricia Grassin, Bernard Duchene, Walid Tabbara
    Pages 98-105

  10. Diffuse tomography: A refined model

    • F. Alberto Grünbaum
    Pages 106-111

  11. Three dimensional reconstructions in inverse obstacle scattering

    • Rainer Kress, Axel Zinn
    Pages 112-125

  12. Mathematical questions of a biomagnetic imaging problem

    • Alfred K. Louis
    Pages 126-132

  13. On variable block algebraic reconstruction techniques

    • Yair Censor
    Pages 133-140

  14. On Volterra-Lotka differential equations and multiplicative algorithms for monotone complementarity problems

    • P. P. B. Eggermont
    Pages 141-152

  15. Constrained regularized least squares problems

    • Tommy Elfving
    Pages 153-166

  16. Multiplicative iterative methods in computed tomography

    • Alvaro R. De Pierro
    Pages 167-186

  17. Remark on the informative content of few measurements

    • P. C. Sabatier
    Pages 187-193

  18. Theorems for the number of zeros of the projection radial modulators of the 2D exponential radon transform

    • W. G. Hawkins, N-C Yang, P. K. Leichner
    Pages 194-214

  19. Evaluation of reconstruction algorithms

    • Gabor T. Herman, Dewey Odhner
    Pages 215-228

  20. Radon transform and analog coding

    • Hidemitsu Ogawa, Itsuo Kumazawa
    Pages 229-241
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Keywords

About this book

The conference was devoted to the discussion of present and future techniques in medical imaging, including 3D x-ray CT, ultrasound and diffraction tomography, and biomagnetic ima- ging. The mathematical models, their theoretical aspects and the development of algorithms were treated. The proceedings contains surveys on reconstruction in inverse obstacle scat- tering, inversion in 3D, and constrained least squares pro- blems.Research papers include besides the mentioned imaging techniques presentations on image reconstruction in Hilbert spaces, singular value decompositions, 3D cone beam recon- struction, diffuse tomography, regularization of ill-posed problems, evaluation reconstruction algorithms and applica- tions in non-medical fields. Contents: Theoretical Aspects: J.Boman: Helgason' s support theorem for Radon transforms-a newproof and a generalization -P.Maass: Singular value de- compositions for Radon transforms- W.R.Madych: Image recon- struction in Hilbert space -R.G.Mukhometov: A problem of in- tegral geometry for a family of rays with multiple reflec- tions -V.P.Palamodov: Inversion formulas for the three-di- mensional ray transform - Medical Imaging Techniques: V.Friedrich: Backscattered Photons - are they useful for a surface - near tomography - P.Grangeat: Mathematical frame- work of cone beam 3D reconstruction via the first derivative of the Radon transform -P.Grassin,B.Duchene,W.Tabbara: Dif- fraction tomography: some applications and extension to 3D ultrasound imaging -F.A.Gr}nbaum: Diffuse tomography: a re- fined model -R.Kress,A.Zinn: Three dimensional reconstruc- tions in inverse obstacle scattering -A.K.Louis: Mathemati- cal questions of a biomagnetic imaging problem - Inverse Problems and Optimization: Y.Censor: On variable block algebraic reconstruction techniques -P.P.Eggermont: On Volterra-Lotka differential equations and multiplicative algorithms for monotone complementary problems

Editors and Affiliations

  • Department of Radiology, University of Pennsylvania, Philadelphia, USA

    Gabor T. Herman

  • Fachbereich Mathematik, Universität des Saarlandes, Saarbrücken, Germany

    Alfred K. Louis

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

    Frank Natterer

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