Sampling Methods

  • Martin Hanke
  • Andreas Kirsch

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...


Impedance Tomography Scattered Field Field Pattern Inverse Scattering Problem Topological Derivative 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Martin Hanke
    • 1
  • Andreas Kirsch
    • 2
  1. 1.Bonn UniversityBonnGermany
  2. 2.Karlsruhe Institute of Technology (KIT)KarlsruheGermany

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