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＜電子ブック＞
Mathematical Methods in Tomography : Proceedings of a Conference held in Oberwolfach, Germany, 5-11 June, 1990 / edited by Gabor T. Herman, Alfred K. Louis, Frank Natterer
(Lecture Notes in Mathematics. ISSN:16179692 ; 1497)

版	1st ed. 1991.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	1991
本文言語	英語
大きさ	X, 270 p : online resource
冊子体	Mathematical methods in tomography : proceedings of a conference held in Oberwolfach, Germany, 5-11 June, 1990 / G.T. Herman, A.K. Louis, F. Natterer, (eds.) ; : gw,: us
著者標目	Herman, Gabor T editor Louis, Alfred K editor Natterer, Frank editor SpringerLink (Online service)
件　名	LCSH:Radiology LCSH:Mathematics LCSH:Numerical analysis LCSH:Mathematical analysis LCSH:Biomathematics FREE:Radiology FREE:Applications of Mathematics FREE:Numerical Analysis FREE:Analysis FREE:Mathematical and Computational Biology
一般注記	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 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 Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/BFb0084502

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