The linearized inverse problem in multifrequency electrical impedance tomography

Giovanni S. Alberti, Habib Ammari, Bangti Jin, Jin Keun Seo, Wenlong Zhang

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency dependence, as is often seen in biological tissues. We discuss reconstruction methods for both fully known and partially known spectral profiles and demonstrate in the latter case the successful employment of difference imaging. We also study the reconstruction with an imperfectly known boundary and show that the multifrequency approach can eliminate modeling errors and recover almost all inclusions. In addition, we develop an efficient group sparse recovery algorithm for the robust solution of related linear inverse problems. Several numerical simulations are presented to illustrate and validate the approach.

Original languageEnglish
Pages (from-to)1525-1551
Number of pages27
JournalSIAM Journal on Imaging Sciences
Volume9
Issue number4
DOIs
Publication statusPublished - 2016 Jan 1

Fingerprint

Electrical Impedance Tomography
Acoustic impedance
Inverse problems
Tomography
Inverse Problem
Inclusion
Linear Inverse Problems
Biological Tissue
Modeling Error
Conductivity
Eliminate
Recovery
Imaging
Tissue
Imaging techniques
Unknown
Numerical Simulation
Computer simulation
Demonstrate
Profile

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Alberti, Giovanni S. ; Ammari, Habib ; Jin, Bangti ; Seo, Jin Keun ; Zhang, Wenlong. / The linearized inverse problem in multifrequency electrical impedance tomography. In: SIAM Journal on Imaging Sciences. 2016 ; Vol. 9, No. 4. pp. 1525-1551.
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The linearized inverse problem in multifrequency electrical impedance tomography. / Alberti, Giovanni S.; Ammari, Habib; Jin, Bangti; Seo, Jin Keun; Zhang, Wenlong.

In: SIAM Journal on Imaging Sciences, Vol. 9, No. 4, 01.01.2016, p. 1525-1551.

Research output: Contribution to journalArticle

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