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Sampling Methods

In: Handbook of Mathematical Methods in Imaging

Author

Listed:
  • Martin Hanke-Bourgeois

    (Johannes Gutenberg-Universität Mainz, Institut für Mathematik)

  • Andreas Kirsch

    (Karlsruhe Institute of Technology (KIT), Department of Mathematics)

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.

Suggested Citation

  • Martin Hanke-Bourgeois & Andreas Kirsch, 2015. "Sampling Methods," Springer Books, in: Otmar Scherzer (ed.), Handbook of Mathematical Methods in Imaging, edition 2, pages 591-647, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-0790-8_12
    DOI: 10.1007/978-1-4939-0790-8_12
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