This book is based on lectures given at a Summer School on inverse problems and their applications, sponsored by CEA (the French Atomic Energy Commission), EDF (Electricite de France) and INRIA (the French National Research Institute for Computer Science and Automation) and held in Breau-Sans-Nappe in July 1985. The lectures are aimed primarily at undergraduate or graduate students and researchers in physics, applied mathematics and engineering who are interested in the fundamental problem of extracting useful information from physical data. The methods described herein are therefore applicable to a multitude of research fields, including medical imaging, astronomy, geophysics, civil engineering, radar sounding and non-destructive testing. In short, this book is a primer for any study in which a large number of parameters are to be extracted from a large number of data.
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Physicists, applied mathematicians and engineers involved in data interpretation, signal processing or imaging (particularly in non-destructive testing) radar, optics, medical imaging, geophysics; graduate students and scientist, mathematicians and engineers entering these fields.
ISBN-13
978-0-85274-285-3 (9780852742853)
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Schweitzer Klassifikation
Image reconstruction from projections - an approach from mathematical analysis (Gabor T Herman and Heang K Tuy): Introduction. Background from mathematical analysis. The radon transform in the space of distributions with compact support. Use of a priori knowledge. Conclusions. Applied Inverse Problems for acoustic, electromagnetic and elastic wave scattering. (Karl J Langenberg): Introduction. Acoustic, electromagnetic and elastic waves. Huygens' principle. Time harmonic plane wave spectra of the homogeneous wave equation. Reconstruction from projections. Rayleigh-Sommerfield-holography. Generalized holography. Coherent superposition of generalised holography experiments. Diffraction tomography. Time domain backpropagation. Monostatic experiments. References. Basic concepts and methods of inverse problems (Pierre C Sabatier): Foundations. Linearized inverse problems. Spectral inverse problems and the Gelfand-Levitan equation. One dimensional inverse scattering problems and the Marchenko equation. Problems and excerises. Appendix - Problems and excercises.
