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3D ELECTRICAL IMPEDANCE TOMOGRAPHY RECONSTRUCTIONS FROM SIMULATED ELECTRODE DATA USING DIRECT INVERSION texp AND

S J Hamilton1, D Isaacson2, V Kolehmainen3

  • 1Department of Mathematical and Statistical Sciences; Marquette University, Milwaukee, WI 53233 USA.

Inverse Problems and Imaging (Springfield, Mo.)
|February 17, 2022
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Summary

The novel t-method for Electrical Impedance Tomography (EIT) is now implemented in 3D using simulated data. This method shows promise for fast, real-time conductivity reconstructions, comparable to existing techniques.

Keywords:
Calderóncomplete electrode modelcomplex geometrical opticsconductivitytexp

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Area of Science:

  • Electrical Impedance Tomography (EIT)
  • Computational Electromagnetics
  • Applied Mathematics

Background:

  • Electrical Impedance Tomography (EIT) enables non-invasive imaging of internal conductivity distributions.
  • Previous t-methods in 2D EIT demonstrated robust real-time conductivity reconstructions.
  • 3D EIT implementations have lagged behind 2D due to computational complexity and data requirements.

Purpose of the Study:

  • To present the first numerical implementation of the t-method for 3D EIT using simulated electrode data.
  • To evaluate the performance of the 3D t-method against established methods like Calderón's, TV, and smoothness regularization.
  • To assess the potential of the 3D t-method for real-time conductivity and permittivity imaging.

Main Methods:

  • Developed a 3D numerical implementation of the t-method for EIT.
  • Utilized tailor-made non-linear Fourier transforms with measured current and voltage data.
  • Applied low-pass filtering in the non-linear Fourier domain for reconstruction stabilization.

Main Results:

  • The 3D t-method successfully reconstructed conductivity and permittivity for disjoint, non-radially symmetric targets.
  • Performance was comparable to the Calderón method and superior to traditional regularization techniques.
  • The method demonstrated robustness with noisy voltage data on spherical domains.

Conclusions:

  • The 3D t-method is a viable and promising approach for EIT reconstructions.
  • It achieves comparable quality to 2D counterparts and offers potential for real-time applications.
  • The fast, non-optimized computational cost makes it suitable for time-sensitive imaging scenarios.