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Erschienen in:
Linear Inverse Problems Kapitel lesen Erstes Kapitel lesen

2015 | OriginalPaper | Buchkapitel

Sampling Methods

verfasst von : Martin Hanke-Bourgeois, Andreas Kirsch

Erschienen in: Handbook of Mathematical Methods in Imaging

Verlag: Springer New York

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Abstract

The topic of this chapter is devoted to shape identification problems, i.e., problems where the shape of an object has to be determined from indirect measurements. In contrast to iterative methods where a sequence of forward problems has to be computed the sampling methods avoid the (usually expansive) computation of the forward problems. Instead, a class of test objects (e.g., points) are chosen and a binary criterium is constructed which depends on the measured data only, and which decides whether this test object is inside or outside of the searched for domain. In this chapter, the factorization method is explained for the impedance tomography problem with insulating or conducting inclusions, for scattering theory for time harmonic acoustic plane waves in the presence of a perfectly sound–soft obstacle, and for electromagnetic scattering by an inhomogeneous conducting medium. Brief descriptions of related sampling methods, such as the linear sampling method, MUSIC, the singular sources method, and the probe method complement this chapter.

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Vorheriges Kapitel Expansion Methods
Nächstes Kapitel Inverse Scattering
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Metadaten
Titel
Sampling Methods
verfasst von
Martin Hanke-Bourgeois
Andreas Kirsch
Copyright-Jahr
2015
Verlag
Springer New York
Buch
Handbook of Mathematical Methods in Imaging

Print ISBN: 978-1-4939-0789-2

Electronic ISBN: 978-1-4939-0790-8

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-1-4939-0790-8_12