Analyticity of point measurements in inverse conductivity and scattering problems

Otto Seiskari

Research output: ThesisDoctoral ThesisCollection of Articles

Abstract

Inverse conductivity and Helmholtz scattering problems with distributional boundary values are studied. In the context of electrical impedance tomography (EIT), the considered concepts can be interpreted in terms of measurements involving point-like electrodes. The notion of bisweep data of EIT, analogous to the far-field pattern in scattering theory, is introduced and applied in the theory of inverse conductivity problems. In particular, it is shown that bisweep data are the Schwartz kernel of the relative Neumann-to-Dirichlet map, and this result is employed in proving new partial data results for Calderon's problem. Similar techniques are also applied in the scattering context in order to prove the joint analyticity of the far-field pattern. Another recent concept, sweep data of EIT, analogous to the far-field backscatter data, is studied further, and a numerical method for locating small inhomogeneities from sweep data is presented. It is also demonstrated how bisweep data and conformal maps can be used to reduce certain numerical inverse conductivity problems in piecewise smooth plane domains to equivalent problems in the unit disk.
Translated title of the contributionPistemittausten analyyttisyys käänteisjohtavuus- ja sirontaongelmissa
Original languageEnglish
QualificationDoctor's degree
Awarding Institution
  • Aalto University
Supervisors/Advisors
  • Hyvönen, Nuutti, Supervising Professor
  • Hyvönen, Nuutti, Thesis Advisor
Publisher
Print ISBNs978-952-60-5383-7
Electronic ISBNs978-952-60-5384-4
Publication statusPublished - 2013
MoE publication typeG5 Doctoral dissertation (article)

Keywords

  • inverse problems
  • electrical impedance tomography
  • point measurements
  • Calderón problem
  • partial data
  • (bi)sweep data
  • elliptic boundary value problems
  • scattering
  • far-field pattern

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