Mathematical methods in tomography : proceedings of a conference held in Oberwolfach, Germany, 5-11 June 1990 / G.T. Herman, A.K. Louis, F. Natterer, eds.

Contributor(s): Herman, Gabor T | Louis, Alfred Karl, 1949- | Natterer, F. (Frank), 1941- | Mathematisches Forschungsinstitut Oberwolfach Material type: Text

Contents:

Helgason's support theorem for Radon transforms : a new proof and a generalization / J. Boman -- Singular value decompositions for Radon transforms / P. Maass -- Image reconstruction in Hilbert space / W.R. Madych -- A problem of integral geometry for a family of rays with multiple reflections / R.G. Mukhometov -- Inversion formulas for the three-dimensional ray transform / V.P. Palamadov -- Backscattered photons : are they useful for a surface-near tomography / V. Friedrich -- Mathematical framework of cone beam 3D reconstruction via the first derivative of the Radon transform / P. Grangeat -- Diffraction tomography : some applications and extension to 3D ultrasound imaging / P. Grassin, B. Duchene, W. Tabbara.

Diffuse tomography : a refined model / F.A. Grünbaum -- Three dimensional reconstructions in inverse obstacle scattering / R. Kress, A. Zinn -- Mathematical questions of a biomagnetic imaging problem / A.K. Louis -- On variable block algebraic reconstruction techniques / Y. Censor -- On Volterra-Lotka differential equations and multiplicative algorithms for monotone complementary problems / P.P.B. Eggermont -- Constrained regularized least squares problems / T. Elfving -- Multiplicative iterative methods in computed tomography / A. de Pierro -- Remark on the informative content of a few measurements / P.C. Sabatier -- Theorems for the number of zeros of the projection radial modulators of the 2D-exponential Radon transform / W.G. Hawkins, N.C. Yang, P.K. Leichner.

Evaluation of reconstruction algorithms / G.T. Herman, D. Odhner -- Radon transform and analog coding / H. Ogawa, I. Kumazawa -- Determination of the specific density of an aerosol through tomography / L.R. Oudin -- Computed tomography and rockets / E.T. Quinto.

Action note: digitized 2010 committed to preserveSummary: 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.

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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.

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