Frank Natterer – författare

Provides a unified view of tomographic techniques, a common mathematical framework, and an in-depth treatment of reconstruction algorithms, focusing on the reconstruction of a function from line or plane integrals, with special emphasis on applications in radiology, science, and engineering. It covers the relevant mathematical theory of the Radon transform and related transforms and also studies more practical questions such as stability, sampling, resolution, and accuracy. Quite a bit of attention is given to the derivation, analysis, and practical examination of reconstruction algorithms, for both standard problems and problems with incomplete data.

The articles collected in this volume are based on lectures given at the IMA Workshop, "Computational Radiology and Imaging: Therapy and Diagnostics", March 17-21, 1997. Introductory articles by the editors have been added. The focus is on inverse problems involving electromagnetic radiation and particle beams, with applications to X-ray tomography, nuclear medicine, near-infrared imaging, microwave imaging, electron microscopy, and radiation therapy planning. Mathematical and computational tools and models which play important roles in this volume include the X-ray transform and other integral transforms, the linear Boltzmann equation and, for near-infrared imaging, its diffusion approximation, iterative methods for large linear and non-linear least-squares problems, iterative methods for linear feasibility problems, and optimization methods. The volume is intended not only for mathematical scientists and engineers working on these and related problems, but also for non-specialists. It contains much introductory expository material, and a large number of references. Many unsolved computational and mathematical problems of substantial practical importance are pointed out.

The articles collected in this volume are based on lectures given at the IMA Workshop, "Computational Radiology and Imaging: Therapy and Diagnostics", March 17-21, 1997. Introductory articles by the editors have been added. The focus is on inverse problems involving electromagnetic radiation and particle beams, with applications to X-ray tomography, nuclear medicine, near-infrared imaging, microwave imaging, electron microscopy, and radiation therapy planning. Mathematical and computational tools and models which play important roles in this volume include the X-ray transform and other integral transforms, the linear Boltzmann equation and, for near-infrared imaging, its diffusion approximation, iterative methods for large linear and non-linear least-squares problems, iterative methods for linear feasibility problems, and optimization methods. The volume is intended not only for mathematical scientists and engineers working on these and related problems, but also for non-specialists. It contains much introductory expository material, and a large number of references. Many unsolved computational and mathematical problems of substantial practical importance are pointed out.

The conference was devoted to the discussion of present andfuture techniques in medical imaging, including 3D x-ray CT,ultrasound and diffraction tomography, and biomagnetic ima-ging. The mathematical models, their theoretical aspects andthe development of algorithms were treated. The proceedingscontains surveys on reconstruction in inverse obstacle scat-tering, inversion in 3D, and constrained least squares pro-blems.Research papers include besides the mentioned imagingtechniques presentations on image reconstruction in Hilbertspaces, singular value decompositions, 3D cone beam recon-struction, diffuse tomography, regularization of ill-posedproblems, evaluation reconstruction algorithms and applica-tions in non-medical fields.Contents: Theoretical Aspects:J.Boman: Helgason'' s support theorem for Radon transforms-anewproof 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 asurface - near tomography - P.Grangeat: Mathematical frame-work of cone beam 3D reconstruction via the first derivativeof the Radon transform -P.Grassin,B.Duchene,W.Tabbara: Dif-fraction tomography: some applications and extension to 3Dultrasound 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 - InverseProblems and Optimization: Y.Censor: On variable blockalgebraic reconstruction techniques -P.P.Eggermont: OnVolterra-Lotka differential equations and multiplicativealgorithms for monotone complementary problems