Lecture Notes in Mathematics

Mathematical Methods in Tomography

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

Editors: Herman, Gabor T., Louis, Alfred K., Natterer, Frank (Eds.)

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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

Table of contents (21 chapters)

Table of contents (21 chapters)

Buy this book

eBook $54.99
price for USA in USD
  • ISBN 978-3-540-46615-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts available
Softcover $69.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Mathematical Methods in Tomography
Book Subtitle
Proceedings of a Conference held in Oberwolfach, Germany, 5-11 June, 1990
Editors
  • Gabor T. Herman
  • Alfred K. Louis
  • Frank Natterer
Series Title
Lecture Notes in Mathematics
Series Volume
1497
Copyright
1991
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-46615-4
DOI
10.1007/BFb0084502
Softcover ISBN
978-3-540-54970-3
Series ISSN
0075-8434
Edition Number
1
Number of Pages
X, 270
Topics