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Mathematical Methods in Tomography

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

  • Gabor T. Herman
  • Alfred K. Louis
  • Frank Natterer

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

Table of contents

  1. Front Matter
    Pages I-X
  2. W. R. Madych
    Pages 15-45
  3. Patricia Grassin, Bernard Duchene, Walid Tabbara
    Pages 98-105
  4. F. Alberto Grünbaum
    Pages 106-111
  5. Gabor T. Herman, Dewey Odhner
    Pages 215-228
  6. Hidemitsu Ogawa, Itsuo Kumazawa
    Pages 229-241
  7. Eric Todd Quinto
    Pages 261-268

About these proceedings

Introduction

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

Keywords

Inverse Problems Medical Radon Transform Tomography algorithms computed tomography (CT) optimization

Editors and affiliations

  • Gabor T. Herman
    • 1
  • Alfred K. Louis
    • 2
  • Frank Natterer
    • 3
  1. 1.Department of RadiologyUniversity of PennsylvaniaPhiladelphiaUSA
  2. 2.Fachbereich MathematikUniversität des SaarlandesSaarbrückenGermany
  3. 3.Institut für Numerische und Instrumentelle MathematikUniversität MünsterMünsterGermany

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0084502
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-54970-3
  • Online ISBN 978-3-540-46615-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site