000 | 05864nam a22005895i 4500 | ||
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001 | 978-3-540-46615-4 | ||
003 | DE-He213 | ||
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007 | cr nn 008mamaa | ||
008 | 121227s1991 gw | s |||| 0|eng d | ||
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_a9783540466154 _9978-3-540-46615-4 |
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024 | 7 |
_a10.1007/BFb0084502 _2doi |
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050 | 4 | _aR895-920 | |
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_aMMPH _2bicssc |
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_aMED008000 _2bisacsh |
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_aMKSH _2thema |
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_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. |
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_aX, 270 p. _bonline resource. |
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_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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_aLecture Notes in Mathematics, _x0075-8434 ; _v1497 |
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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. |
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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 |
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_aAnalysis. _0http://scigraph.springernature.com/things/product-market-codes/M12007 |
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_aPhysiological, Cellular and Medical Topics. _0http://scigraph.springernature.com/things/product-market-codes/M31020 |
700 | 1 |
_aHerman, Gabor T. _eeditor. _4edt _4http://id.loc.gov/vocabulary/relators/edt |
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700 | 1 |
_aLouis, Alfred K. _eeditor. _4edt _4http://id.loc.gov/vocabulary/relators/edt |
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700 | 1 |
_aNatterer, Frank. _eeditor. _4edt _4http://id.loc.gov/vocabulary/relators/edt |
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710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
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_iPrinted edition: _z9783540549703 |
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_iPrinted edition: _z9783662193631 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1497 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/BFb0084502 |
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