Skip to main content
  • Conference proceedings
  • © 1991

Mathematical Methods in Tomography

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

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

Buying options

eBook USD 54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

This is a preview of subscription content, access via your institution.

Table of contents (21 papers)

  1. Front Matter

    Pages I-X
  2. Image reconstruction in Hilbert space

    • W. R. Madych
    Pages 15-45
  3. Diffraction tomography some applications and extension to 3-D ultrasound imaging

    • Patricia Grassin, Bernard Duchene, Walid Tabbara
    Pages 98-105
  4. Diffuse tomography: A refined model

    • F. Alberto Grünbaum
    Pages 106-111
  5. Evaluation of reconstruction algorithms

    • Gabor T. Herman, Dewey Odhner
    Pages 215-228
  6. Radon transform and analog coding

    • Hidemitsu Ogawa, Itsuo Kumazawa
    Pages 229-241

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

Keywords

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

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

Bibliographic Information

Buying options

eBook USD 54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions