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Mathematical Methods in Tomography
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 proceeding...
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Lenguaje: | eng |
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Springer
1991
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Acceso en línea: | https://dx.doi.org/10.1007/BFb0084502 http://cds.cern.ch/record/1696169 |
_version_ | 1780936068291362816 |
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author | Herman, Gabor Louis, Alfred Natterer, Frank |
author_facet | Herman, Gabor Louis, Alfred Natterer, Frank |
author_sort | Herman, Gabor |
collection | CERN |
description | 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 |
id | cern-1696169 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 1991 |
publisher | Springer |
record_format | invenio |
spelling | cern-16961692021-04-22T07:05:27Zdoi:10.1007/BFb0084502http://cds.cern.ch/record/1696169engHerman, GaborLouis, AlfredNatterer, FrankMathematical Methods in TomographyMathematical Physics and MathematicsThe 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 problemsSpringeroai:cds.cern.ch:16961691991 |
spellingShingle | Mathematical Physics and Mathematics Herman, Gabor Louis, Alfred Natterer, Frank Mathematical Methods in Tomography |
title | Mathematical Methods in Tomography |
title_full | Mathematical Methods in Tomography |
title_fullStr | Mathematical Methods in Tomography |
title_full_unstemmed | Mathematical Methods in Tomography |
title_short | Mathematical Methods in Tomography |
title_sort | mathematical methods in tomography |
topic | Mathematical Physics and Mathematics |
url | https://dx.doi.org/10.1007/BFb0084502 http://cds.cern.ch/record/1696169 |
work_keys_str_mv | AT hermangabor mathematicalmethodsintomography AT louisalfred mathematicalmethodsintomography AT nattererfrank mathematicalmethodsintomography |