Mathematical methods in tomography
Subtitle: proceedings of a conference held in Oberwolfach, 5-11 June 1990
By: G. Herman, A.K. Louis, F. Natterer, eds.
Contributors: Herman, Gabor T.; Louis, Alfred K. 1949-; Natterer, F. 1941-; Mathematisches Fotschungsinstitut Oberwolfach.
Series: Lecture notes in mathematics ;; 1497; Lecture notes in mathematics (Springer-Verlag) ;; 1497.
Publisher: Springer-Verlag
Published: 1991
Place of publication: Berlin; New York
Language: eng
Number of pages: 268
Subjects: Radon transforms -- Congresses; Tomography -- Mathematics -- Congresses
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
Notes: Includes bibliographical references.
Based on selected lectures delivered at the August 1990 conference held at the Mathematisches Forschungsinstitut at Oberwolfach.