## Basic methods of tomography and inverse problems: a set of lecturesThis 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. |

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### Contents

Background from Mathematical Analysis | 21 |

The Radon Transform in the Space of Distributions with Compact | 69 |

Use of A Priori Knowledge | 103 |

Copyright | |

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### Common terms and phrases

algorithm backprojection bistatic far-field image bounded compact support compare fig components computed computerized tomography continuous convergence convex convolution corresponding defined denotes derive Diffraction Slice Theorem diffraction tomography diversity bistatic far-field domain backpropagation eigenvalues evanescent wave Ewald-sphere far-field inverse scattering filtered backpropagation finite formula Fourier Diffraction Slice Fourier space Fourier transform frequency diversity Frequency diversity bistatic given Green's function harmonic Hence Hilbert space holographic holographic image Huygens IEEE Trans image of rigid impulse response incident field integral equation inverse problem inverse scattering problem K-space kernel Lemma linear operator mapping mathematical measurement surface method monostatic far-field norm obtain P-wave parameters physical optics planar plane wave Porter-Bojarski propagation Radon transform Rayleigh-Sommerfeld reconstruction result satisfies scalar scattered field secondary sources sequence solution spatial Fourier spectral function subset tempered distribution threedimensional tion values vector wave equation wavefields weak scatterer yields zero