Gabor T. Herman & Alfred K. Louis 
Mathematical Methods in Tomography [PDF ebook] 
Proceedings of a Conference held in Oberwolfach, Germany, 5-11 June, 1990

The conference was devoted to the discussion of present andfuture techniques in medical imaging, including 3D x-ray CT, ultrasound and diffraction tomography, and biomagnetic ima-ging. The mathematical models, their theoretical aspects andthe development of algorithms were treated. The proceedingscontains surveys on reconstruction in inverse obstacle scat-tering, inversion in 3D, and constrained least squares pro-blems.Research papers include besides the mentioned imagingtechniques presentations on image reconstruction in Hilbertspaces, singular value decompositions, 3D cone beam recon-struction, diffuse tomography, regularization of ill-posedproblems, evaluation reconstruction algorithms and applica-tions in non-medical fields. Contents: Theoretical Aspects:J.Boman: Helgason’ s support theorem for Radon transforms-anewproof 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 asurface – near tomography – P.Grangeat: Mathematical frame-work of cone beam 3D reconstruction via the first derivativeof the Radon transform -P.Grassin, B.Duchene, W.Tabbara: Dif-fraction tomography: some applications and extension to 3Dultrasound 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 blockalgebraic reconstruction techniques -P.P.Eggermont: On Volterra-Lotka differential equations and multiplicativealgorithms for monotone complementary problems