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On sparse forward solutions in non-stationary domains for the EIT imaging problem.

Panagiotis Kantartzis1, Panos Liatsis

  • 1Information Engineering and Medical Imaging Group, City University London, Northampton square, EC1V 0HB London, UK. p.kantartzis@city.ac.uk

Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference
|January 19, 2012
PubMed
Summary

This study introduces wavelet basis functions to Electrical Impedance Tomography (EIT) forward problems, significantly reducing computational costs. Wavelets enable sparse approximations, drastically cutting down the number of required coefficients for faster image reconstruction.

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Area of Science:

  • Electrical Impedance Tomography (EIT)
  • Computational Electromagnetics
  • Numerical Analysis

Background:

  • Electrical Impedance Tomography (EIT) forward problems require solving elliptic partial differential equations.
  • The Finite Element Method (FEM) is commonly used but faces challenges with increasing model complexity and computational demands.
  • Existing methods often rely on piece-wise linear basis functions and domain reduction techniques to manage computational load.

Purpose of the Study:

  • To develop a more computationally efficient method for solving EIT forward problems.
  • To explore the use of wavelet basis functions for sparse approximations in EIT.
  • To assess the impact of this new approach on the overall EIT image reconstruction process.

Main Methods:

  • Replaced traditional piece-wise linear basis functions with wavelet basis functions.
  • Employed the domain embedding method in conjunction with wavelets.
  • Focused on enabling sparse approximations for forward computations in EIT.

Main Results:

  • Achieved significant computational savings in forward problem calculations.
  • Demonstrated that less than 5% of coefficients are needed for practical computations.
  • Maintained an O(N) complexity for the forward problem, enabling faster processing.
  • Showcased the practical applicability of wavelet-based sparse approximations.

Conclusions:

  • Wavelet basis functions offer a computationally efficient alternative to traditional methods for EIT forward problems.
  • The proposed scheme significantly reduces the number of required coefficients and computational resources.
  • This approach has a positive impact on the inverse problem, paving the way for faster EIT image reconstruction.
  • The method's independence from specific wavelet families enhances its versatility.