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Published in:
Linear Inverse Problems Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Sampling Methods

Authors : Martin Hanke-Bourgeois, Andreas Kirsch

Published in: Handbook of Mathematical Methods in Imaging

Publisher: 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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previous chapter Expansion Methods
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Appendix
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Metadata
Title
Sampling Methods
Authors
Martin Hanke-Bourgeois
Andreas Kirsch
Copyright Year
2015
Publisher
Springer New York
Book
Handbook of Mathematical Methods in Imaging

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

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

Copyright Year: 2015

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

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