Factorization method and its physical justification in frequency-difference electrical impedance tomography

Bastian Harrach, Jin Keun Seo, Eung Je Woo

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34 Citations (Scopus)


Time-difference electrical impedance tomography (tdEIT) requires two data sets measured at two different times. The difference between them is utilized to produce images of time-dependent changes in a complex conductivity distribution inside the human body. Frequency-difference EIT (fdEIT) was proposed to image frequency-dependent changes of a complex conductivity distribution. It has potential applications in tumor and stroke imaging since it can visualize an anomaly without requiring any time-reference data obtained in the absence of an anomaly. In this paper, we provide a rigorous analysis for the detectability of an anomaly based on a constructive and quantitative physical correlation between a measured fdEIT data set and an anomaly. From this, we propose a new noniterative frequency-difference anomaly detection method called the factorization method (FM) and elaborate its physical justification. To demonstrate its practical applicability, we performed fdEIT phantom imaging experiments using a multifrequency EIT system. Applying the FM to measured frequency-difference boundary voltage data sets, we could quantitatively evaluate indicator functions inside the imaging domain, of which values at each position reveal presence or absence of an anomaly. We found that the FM successfully localizes anomalies inside an imaging domain with a frequency-dependent complex conductivity distribution. We propose the new FM as an anomaly detection algorithm in fdEIT for potential applications in tumor and stroke imaging.

Original languageEnglish
Article number5491179
Pages (from-to)1918-1926
Number of pages9
JournalIEEE Transactions on Medical Imaging
Issue number11
Publication statusPublished - 2010 Nov

Bibliographical note

Funding Information:
Manuscript received January 10, 2010; revised March 23, 2010, May 29, 2010; accepted June 10, 2010. Date of publication June 21, 2010; date of current version November 03, 2010. This work was conducted while B. Harrach was employed at the Institut für Mathematik, Johannes Gutenberg-Universität Mainz, Germany and supported by the German Federal Ministry of Education and Research (BMBF) under Grant 03HBPAM2 (Regularization techniques for electrical impedance tomography in medical and geological sciences). J. K. Seo was supported by the WCU program through NRF (R31-2008-000-10049-0). J. K. Seo and E. J. Woo were supported by the SRC/ERC program of MOST/NRF (R11-2002-103). Asterisk indicates corresponding author. *B. Harrach is with the Fakultät für Mathematik, Technische Universität München, 85748 Garching, Germany (e-mail: harrach@ma.tum.de).

All Science Journal Classification (ASJC) codes

  • Software
  • Radiological and Ultrasound Technology
  • Computer Science Applications
  • Electrical and Electronic Engineering


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