Mathematical Methods in Tomography: Proceedings of a Conference held in Oberwolfach, Germany, 5-11 June, 1990 by Gabor T. HermanMathematical Methods in Tomography: Proceedings of a Conference held in Oberwolfach, Germany, 5-11 June, 1990 by Gabor T. Herman

Mathematical Methods in Tomography: Proceedings of a Conference held in Oberwolfach, Germany, 5-11…

EditorGabor T. Herman, Alfred K. Louis, Frank Natterer

Paperback | January 15, 1992

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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 - InverseProblems and Optimization: Y.Censor: On variable blockalgebraic reconstruction techniques -P.P.Eggermont: OnVolterra-Lotka differential equations and multiplicativealgorithms for monotone complementary problems
Title:Mathematical Methods in Tomography: Proceedings of a Conference held in Oberwolfach, Germany, 5-11…Format:PaperbackDimensions:280 pages, 9.25 × 6.1 × 0.04 inPublished:January 15, 1992Publisher:Springer Berlin HeidelbergLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3540549706

ISBN - 13:9783540549703

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Table of Contents

From the Contents: Theoretical Aspects: J. Boman: Helgason's support theorem for Radon transforms - a new proof and a generalization.- P. Maaß: Singular value decompositions for Radon transforms.- W.R. Madych: Image reconstruction in Hilbert space.- R.G. Mukhometov: A problem of integral geometry for a family of rays with multiple reflections.- V.P. Palamodov: Inversion formulas for the three-dimensional ray transform. Medical Imaging Techniques: V. Friedrich: Backscattered Photons - are they useful for a surface - near tomography.- P. Grangeat: Mathematical framework of cone beam 3D reconstruction via the first derivative of the Radon transform.- P. Grassin, B. Duchene, W. Tabbara: Diffraction tomography: some applications and extension to 3D ultrasound imaging.- F.A. Grünbaum: Diffuse tomography: a refined model.- R. Kress, A. Zinn: Three dimensional reconstructions in inverse obstacle scattering.- A.K. Louis: Mathematical questions of a biomagnetic imaging problem. Inverse Problems and Optimization: Y. Censor: On variable block algebraic reconstruction techniques.- P.P.B. Eggermont: On Volterra-Lotka differential equations and multiplicative algorithms for monotone complementary problems.