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Handbook of Mathematical Methods in Imaging pp 501–550Cite as

Sampling Methods

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Introduction and Historical Background

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. Such a situation typically occurs in problems of tomography, in particular electrical impedance tomography or optical tomography. For example, a current through a homogeneous object will in general induce a different potential than the same current through the same object containing an enclosed cavity. In impedance tomography, the task is to determine the shape of the cavity from measurements of the potential on the boundary of the object. For survey articles on this subject we refer to [18], [55], and to Chap. 14 in this volume.

As a second of these fields we mention inverse scattering problemswhere one wants to detect – and identify – unknown objects through the use of acoustic, electromagnetic, or elastic waves. Similar to above, one of the important problems in inverse scattering...

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Author information

Authors and Affiliations

  1. Bonn University, Bonn, Germany

    Martin Hanke

  2. Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany

    Andreas Kirsch

Authors
  1. Martin Hanke
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  2. Andreas Kirsch
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Editors and Affiliations

  1. Computational Science Center, University of Vienna, Nordbergstrasse 15, Vienna, Austria

    Otmar Scherzer

  2. RICAM, Austrian Academy of Sciences, Linz, Austria

    Otmar Scherzer

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Hanke, M., Kirsch, A. (2011). Sampling Methods. In: Scherzer, O. (eds) Handbook of Mathematical Methods in Imaging. Springer, New York, NY. https://doi.org/10.1007/978-0-387-92920-0_12

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