Mathematical Methods in Tomography / Lecture Notes in Mathematics Bd.1497 (PDF)

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