Mathematical methods in tomography : proceedings of a conference held in Oberwolfach, Germany, 5-11 June, 1990
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書誌事項
Mathematical methods in tomography : proceedings of a conference held in Oberwolfach, Germany, 5-11 June, 1990
（Lecture notes in mathematics, 1497）
Springer-Verlag, c1991
- : gw
- : us
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注記
Based on selected lectures delivered at the August 1990 conference held at the Mathematisches Forschungsinstitut at Oberwolfach
Includes bibliographical references
内容説明・目次
内容説明
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
目次
Helgason'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.
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