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Computed Tomography01:10

Computed Tomography

Tomography refers to imaging by sections. Computed tomography (CT) is a non-invasive imaging technique that uses computers to analyze several cross-sectional X-rays to reveal minute details about structures in the body.
The technique was invented in the 1970s and is based on the principle that as X-rays pass through the body, they are absorbed or reflected at different levels. In the technique, a patient lies on a motorized platform while a computerized axial tomography (CAT) scanner rotates...

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Related Experiment Video

Updated: May 7, 2026

Monitoring Lung Function with Electrical Impedance Tomography in the Intensive Care Unit
05:56

Monitoring Lung Function with Electrical Impedance Tomography in the Intensive Care Unit

Published on: September 6, 2024

Recent progress on the factorization method for electrical impedance tomography.

Bastian Harrach1

  • 1Department of Mathematics, University of Würzburg, 97074 Würzburg, Germany.

Computational and Mathematical Methods in Medicine
|September 27, 2013
PubMed
Summary
This summary is machine-generated.

The Factorization Method offers a direct way to locate conductivity anomalies in electrical impedance tomography (EIT). This work simplifies its theory and presents an advanced formulation for continuous data and complex conductivities.

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Area of Science:

  • Applied Mathematics
  • Electrical Engineering
  • Medical Imaging

Background:

  • The Factorization Method, initially for inverse scattering, was adapted for Electrical Impedance Tomography (EIT) by Brühl and Hanke.
  • Significant theoretical advancements have refined the Factorization Method for EIT since its inception.
  • Previous formulations often required strong assumptions and complex proofs.

Purpose of the Study:

  • To provide a comprehensive summary of the progress in the Factorization Method for EIT.
  • To present a current, state-of-the-art formulation of the Factorization Method tailored for continuous EIT data.
  • To extend the method's applicability to general piecewise analytic conductivities with simplified proofs.

Main Methods:

  • The study focuses on a noniterative approach to identify conductivity anomalies.
  • It builds upon the foundational work of Kirsch, Brühl, and Hanke in inverse problems and EIT.
  • The core methodology involves developing simplified, self-contained proofs for theoretical underpinnings.

Main Results:

  • The Factorization Method is presented as a robust, noniterative technique for EIT.
  • The formulation is adapted for continuous data, enhancing practical applicability.
  • The method is successfully formulated for piecewise analytic conductivities, broadening its scope.

Conclusions:

  • This work offers a unified and simplified theoretical framework for the Factorization Method in EIT.
  • The presented formulation represents a significant advancement for analyzing conductivity anomalies with continuous data.
  • The simplified proofs and extended applicability make the Factorization Method more accessible and powerful for EIT research.