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

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

ISBN 10: 3540549706 / ISBN 13: 9783540549703

Editore: Springer-Verlag Berlin And Heidelberg Gmbh & Co. Kg, 1992

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1991 edition. 278 pages. 9.20x6.20x0.80 inches. In Stock.

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Dati bibliografici

• Titolo: Mathematical Methods in Tomography: Proceedings of a Conference Held in Oberwolfach, Germany, 5-11 June, 1990
• Editore: Springer-Verlag Berlin And Heidelberg Gmbh & Co. Kg
• Data di pubblicazione: 1992
• Lingua: Inglese
• ISBN 10: 3540549706
• ISBN 13: 9783540549703
• Rilegatura: Paperback
• Condizione: Brand New
• Peso: 0,41 chilogrammi

Descrizione articolo

Riassunto

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

Contenuti

Helgason's support theorem for Radon transforms — A new proof and a generalization.- Singular value decompositions for Radon transforms.- Image reconstruction in Hilbert space.- A problem of integral geometry for a family of rays with multiple reflections.- Inversion formulas for the three-dimensional ray transform.- Backscattered photons — Are they useful for a surface-near tomography?.- Mathematical framework of cone beam 3D reconstruction via the first derivative of the radon transform.- Diffraction tomography some applications and extension to 3-D ultrasound imaging.- Diffuse tomography: A refined model.- Three dimensional reconstructions in inverse obstacle scattering.- Mathematical questions of a biomagnetic imaging problem.- On variable block algebraic reconstruction techniques.- On Volterra-Lotka differential equations and multiplicative algorithms for monotone complementarity problems.- Constrained regularized least squares problems.- Multiplicative iterative methods in computed tomography.- Remark on the informative content of few measurements.- Theorems for the number of zeros of the projection radial modulators of the 2D exponential radon transform.- Evaluation of reconstruction algorithms.- Radon transform and analog coding.- Determination of the specific density of an aerosol through tomography.- Computed tomography and rockets.