Limited-angle acousto-electrical tomography

Simon Hubmer, Kim Knudsen, Changyou Li, Ekaterina Sherina*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

This paper considers the reconstruction problem in acoustoelectrical tomography, i.e. the problem of estimating a spatially varying conductivity in a bounded domain from measurements of the internal power densities resulting from different prescribed boundary conditions. Particular emphasis is placed on the limited-angle scenario, in which the boundary conditions are supported only on a part of the boundary. The reconstruction problem is formulated as an optimization problem in a Hilbert space setting and solved using Landweber iteration. The resulting algorithm is implemented numerically in two spatial dimensions and tested on simulated data. The results quantify the intuition that features close to the measurement boundary are stably reconstructed and features further away are less well reconstructed. Finally, the ill-posedness of the limited angle problem is quantified numerically using the singular value decomposition of the corresponding linearized problem.
Original languageEnglish
JournalInverse Problems in Science and Engineering
Volume27
Issue number9
Pages (from-to)1248-1317
Number of pages19
ISSN1741-5977
DOIs
Publication statusPublished - 2018

Keywords

  • Electrical impedance tomography
  • Acousto-electrical tomography
  • Limited-angle
  • Hybrid data
  • Inverse problem
  • Parameter identification
  • Landweber iteration
  • Regularization methods

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