Mathematical Methods in Tomography | Proceedings of a Conference held in Oberwolfach, Germany, 5-11 June, 1990 | ISBN 9783540466154

Mathematical Methods in Tomography

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

herausgegeben von Gabor T. Herman, Alfred K. Louis und Frank Natterer
Mitwirkende
Herausgegeben vonGabor T. Herman
Herausgegeben vonAlfred K. Louis
Herausgegeben vonFrank Natterer
Buchcover Mathematical Methods in Tomography  | EAN 9783540466154 | ISBN 3-540-46615-0 | ISBN 978-3-540-46615-4

Mathematical Methods in Tomography

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

herausgegeben von Gabor T. Herman, Alfred K. Louis und Frank Natterer
Mitwirkende
Herausgegeben vonGabor T. Herman
Herausgegeben vonAlfred K. Louis
Herausgegeben vonFrank Natterer
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