Open Access3D Electrical Impedance Tomography reconstructions from simulated electrode data using direct inversion $ \mathbf{t}^{\rm{{\textbf{exp}}}} $ and Calderón methods
Author(s) -
Sarah J. Hamilton,
David Isaacson,
Ville Kolehmainen,
Peter A. Muller,
J. Toivanen,
Patrick F. Bray
Publication year - 2021
Publication title -
inverse problems and imaging
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.755
H-Index - 40
eISSN - 1930-8345
pISSN - 1930-8337
DOI - 10.3934/ipi.2021032
Subject(s) - electrical impedance tomography , algorithm , fourier transform , electrical impedance , smoothness , regularization (linguistics) , voltage , electrode , inversion (geology) , tomography , mathematical analysis , computer science , physics , materials science , mathematics , optics , geology , artificial intelligence , quantum mechanics , paleontology , structural basin
The first numerical implementation of a \begin{document}$ \mathbf{t}^{\rm{{\textbf{exp}}}} $\end{document} method in 3D using simulated electrode data is presented. Results are compared to Calderón's method as well as more common TV and smoothness regularization-based methods. The \begin{document}$ \mathbf{t}^{\rm{{\textbf{exp}}}} $\end{document} method for EIT is based on tailor-made non-linear Fourier transforms involving the measured current and voltage data. Low-pass filtering in the non-linear Fourier domain is used to stabilize the reconstruction process. In 2D, \begin{document}$ \mathbf{t}^{\rm{{\textbf{exp}}}} $\end{document} methods have shown great promise for providing robust real-time absolute and time-difference conductivity reconstructions but have yet to be used on practical electrode data in 3D, until now. Results are presented for simulated data for conductivity and permittivity with disjoint non-radially symmetric targets on spherical domains and noisy voltage data. The 3D \begin{document}$ \mathbf{t}^{\rm{{\textbf{exp}}}} $\end{document} and Calderón methods are demonstrated to provide comparable quality to their 2D counterparts and hold promise for real-time reconstructions due to their fast, non-optimized, computational cost. Erratum: The name of the fifth author has been corrected from Jussi Toivainen to Jussi Toivanen. We apologize for any inconvenience this may cause.