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

Mathematical Methods in Tomography

Proceedings of a Conference Held in Oberwolfach, Germany, 5-11 June, 1990

By: Gabor T. Herman (Editor), Alfred K. Louis (Editor), Frank Natterer (Editor)

Paperback

Published: 15th January 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

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. Grunbaum: 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.

ISBN: 9783540549703
ISBN-10: 3540549706
Series: Lecture Notes in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 270
Published: 15th January 1992
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.52
Weight (kg): 0.4