Mathematical Methods in Tomography

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