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<p>Electrical impedance tomography (EIT) is a method of internal imaging that requires fast, reliable reconstruction algorithms, especially as wearable technology becomes more popular. We introduce consecutive improvements to the historic Wexler scheme. Firstly, we express it in a form suitable for the finite element method. Furthermore, the algorithm is overrelaxed. The step size is variable and depends on the change in the gradient of the objective function, which improves convergence. The new, simpler electrode model further enhances image quality. We also propose a method for finding the initial conductivity. Those changes bring the scheme on par with standard algorithms such as NOSER and Gauss-Newton with total variational regularization. Moreover, we demonstrate its ability to scale with large-mesh tests.</p>

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An improved Wexler algorithm for electrical impedance tomography using finite element method and gradient based overrelaxation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月6日

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  • Maciej Jurgielewicz,
  • Cezary J. Walczyk

摘要

Electrical impedance tomography (EIT) is a method of internal imaging that requires fast, reliable reconstruction algorithms, especially as wearable technology becomes more popular. We introduce consecutive improvements to the historic Wexler scheme. Firstly, we express it in a form suitable for the finite element method. Furthermore, the algorithm is overrelaxed. The step size is variable and depends on the change in the gradient of the objective function, which improves convergence. The new, simpler electrode model further enhances image quality. We also propose a method for finding the initial conductivity. Those changes bring the scheme on par with standard algorithms such as NOSER and Gauss-Newton with total variational regularization. Moreover, we demonstrate its ability to scale with large-mesh tests.