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020 _a9783540466154
_9978-3-540-46615-4
024 7 _a10.1007/BFb0084502
_2doi
050 4 _aR895-920
072 7 _aMMPH
_2bicssc
072 7 _aMED008000
_2bisacsh
072 7 _aMKSH
_2thema
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082 0 4 _a616.0757
_223
245 1 0 _aMathematical Methods in Tomography
_h[electronic resource] :
_bProceedings of a Conference held in Oberwolfach, Germany, 5–11 June, 1990 /
_cedited by Gabor T. Herman, Alfred K. Louis, Frank Natterer.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1991.
300 _aX, 270 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1497
505 0 _aHelgason'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.
520 _aThe 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.
650 0 _aRadiology, Medical.
650 0 _aMathematics.
650 0 _aNumerical analysis.
650 0 _aGlobal analysis (Mathematics).
650 0 _aPhysiology
_xMathematics.
650 1 4 _aImaging / Radiology.
_0http://scigraph.springernature.com/things/product-market-codes/H29005
650 2 4 _aApplications of Mathematics.
_0http://scigraph.springernature.com/things/product-market-codes/M13003
650 2 4 _aNumerical Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M14050
650 2 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
650 2 4 _aPhysiological, Cellular and Medical Topics.
_0http://scigraph.springernature.com/things/product-market-codes/M31020
700 1 _aHerman, Gabor T.
_eeditor.
_4edt
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700 1 _aLouis, Alfred K.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aNatterer, Frank.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540549703
776 0 8 _iPrinted edition:
_z9783662193631
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1497
856 4 0 _uhttps://doi.org/10.1007/BFb0084502
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