LEADER 05350nam 2200637 450 001 996466756003316 005 20231214170027.0 010 $a3-540-46615-0 024 7 $a10.1007/BFb0084502 035 $a(CKB)1000000000437097 035 $a(SSID)ssj0000324685 035 $a(PQKBManifestationID)12098554 035 $a(PQKBTitleCode)TC0000324685 035 $a(PQKBWorkID)10314293 035 $a(PQKB)10017922 035 $a(DE-He213)978-3-540-46615-4 035 $a(MiAaPQ)EBC5595326 035 $a(Au-PeEL)EBL5595326 035 $a(OCoLC)1076258509 035 $a(MiAaPQ)EBC6842325 035 $a(Au-PeEL)EBL6842325 035 $a(PPN)155176358 035 $a(EXLCZ)991000000000437097 100 $a20220908d1991 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 00$aMathematical methods in tomography $eproceedings of a conference held in Oberwolfach, Germany, 5-11 June 1990 /$fGabor T. Herman, Alfred K. Louis, Frank Natterer, editors 205 $a1st ed. 1991. 210 1$aBerlin ;$aHeidelberg :$cSpringer-Verlag,$d[1991] 210 4$dİ1991 215 $a1 online resource (X, 270 p.) 225 1 $aLecture Notes in Mathematics ;$vVolume 1497 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-54970-6 327 $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. 330 $aThe conference was devoted to the discussion of present and future techniques in medical imaging, including 3D x-ray CT, ultrasound and diffraction tomography, and biomagnetic imaging. The mathematical models, their theoretical aspects and the development of algorithms were treated. The proceedings contains surveys on reconstruction in inverse obstacle scattering, inversion in 3D, and constrained least squares problems. Research papers include besides the mentioned imaging techniques presentations on image reconstruction in Hilbert spaces, singular value decompositions, 3D cone beam reconstruction, diffuse tomography, regularization of ill-posed problems, evaluation reconstruction algorithms and applications in non-medical fields. Contents: Theoretical Aspects: J.Boman: Helgason' s support theorem for Radon transforms-a new proof and a generalization -P.Maass: Singular value de- compositions for Radon transforms- W.R. Madych: Image reconstruction in Hilbert space -R.G. Mukhometov: A problem of integral geometry for a family of rays with multiple reflections -V.P. Palamodov: Inversion formulas for the three-dimensional ray transform - Medical Imaging Techniques: V. Friedrich: Backscattered Photons - are they useful for a surface - near tomography - P.Grangeat: Mathematical frame- work of cone beam 3D reconstruction via the first derivative of the Radon transform -P.Grassin, B.Duchene, W.Tabbara: Dif- fraction tomography: some applications and extension to 3D ultrasound imaging -F.A.Gr}nbaum: Diffuse tomography: a refined model -R.Kress,A.Zinn: Three dimensional reconstructions in inverse obstacle scattering -A.K.Louis: Mathematical questions of a biomagnetic imaging problem - Inverse Problems and Optimization: Y.Censor: On variable block algebraic reconstruction techniques -P.P.Eggermont: On Volterra-Lotka differential equations and multiplicative algorithms for monotone complementary problems. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$vVolume 1497. 606 $aGeometric tomography$vCongresses 606 $aRadon transforms$vCongresses 615 0$aGeometric tomography 615 0$aRadon transforms 676 $a616.075701515357 702 $aHerman$b Gabor T. 702 $aLouis$b Alfred Karl$f1949- 702 $aNatterer$b F$g(Frank),$f1941- 712 02$aMathematisches Forschungsinstitut Oberwolfach. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466756003316 996 $aMathematical methods in tomography$955854 997 $aUNISA