Sparsity prior for electrical impedance tomography with partial data

Henrik Garde, Kim Knudsen

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

This paper focuses on prior information for improved sparsity reconstruction in electrical impedance tomography with partial data, i.e. Cauchy data measured on subsets of the boundary. Sparsity is enforced using an (Formula presented.) norm of the basis coefficients as the penalty term in a Tikhonov functional, and prior information is incorporated by applying a spatially distributed regularization parameter. The resulting optimization problem allows great flexibility with respect to the choice of measurement subsets of the boundary and incorporation of prior knowledge. In fact, the measurement subsets can be chosen completely arbitrary. The problem is solved using a generalized conditional gradient method applying soft thresholding. Numerical examples with noisy simulated data show that the addition of prior information in the proposed algorithm gives vastly improved reconstructions, even for the partial data problem. Moreover, numerical examples show that a reliable reconstruction for the partial data problem can only be found close to the measurement subsets. The method is in addition compared to a total variation approach.
Original languageEnglish
JournalInverse Problems in Science and Engineering
Volume24
Issue number3
Pages (from-to)524-541
Number of pages18
ISSN1741-5977
DOIs
Publication statusPublished - 2016

Keywords

  • electrical impedance tomography
  • ill-posed problem
  • inverse boundary value problem
  • partial data
  • sparsity
  • Boundary value problems
  • Electric impedance
  • Electric impedance measurement
  • Electric impedance tomography
  • Gradient methods
  • Optimization
  • Set theory
  • Tomography
  • Electrical impedance tomography
  • Ill posed problem
  • Inverse boundary value problem
  • Partial data
  • Inverse problems

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