Mathematical Methods in Tomography: Proceedings of a Conference held in Oberwolfach, Germany, 5-11 June, 1990

by Gabor T. Herman (Editor)

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. Theoretical Helgason' s support theorem for Radon transforms-a newproof and a generalization - Singular value de- compositions for Radon transforms- Image recon- struction in Hilbert space - A problem of in- tegral geometry for a family of rays with multiple reflec- tions - Inversion formulas for the three-di- mensional ray transform - Medical Imaging Backscattered Photons - are they useful for a surface - near tomography - Mathematical frame- work of cone beam 3D reconstruction via the first derivative of the Radon transform -P.Grassin,B.Duchene, Dif- fraction some applications and extension to 3D ultrasound imaging -F.A.Gr} Diffuse a re- fined model -R.Kress, Three dimensional reconstruc- tions in inverse obstacle scattering - Mathemati- cal questions of a biomagnetic imaging problem - Inverse Problems and On variable block algebraic reconstruction techniques - On Volterra-Lotka differential equations and multiplicative algorithms for monotone complementary problems

280 pages, Paperback

First published February 1, 1992