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