3D Electrical Impedance Tomography reconstructions from simulated electrode data using direct inversion $ \mathbf{t}^{\rm{{\textbf{exp}}}} $ and Calderón methods

Abstract

<p style='text-indent:20px;'>The first numerical implementation of a <inline-formula><tex-math id="M2">\begin{document}$ \mathbf{t}^{\rm{{\textbf{exp}}}} $\end{document}</tex-math></inline-formula> method in 3D using simulated electrode data is presented. Results are compared to Calderón's method as well as more common TV and smoothness regularization-based methods. The <inline-formula><tex-math id="M3">\begin{document}$ \mathbf{t}^{\rm{{\textbf{exp}}}} $\end{document}</tex-math></inline-formula> method for EIT is based on tailor-made non-linear Fourier transforms involving the measured current and voltage data. Low-pass filtering in the non-linear Fourier domain is used to stabilize the reconstruction process. In 2D, <inline-formula><tex-math id="M4">\begin{document}$ \mathbf{t}^{\rm{{\textbf{exp}}}} $\end{document}</tex-math></inline-formula> methods have shown great promise for providing robust real-time absolute and time-difference conductivity reconstructions but have yet to be used on practical electrode data in 3D, until now. Results are presented for simulated data for conductivity and permittivity with disjoint non-radially symmetric targets on spherical domains and noisy voltage data. The 3D <inline-formula><tex-math id="M5">\begin{document}$ \mathbf{t}^{\rm{{\textbf{exp}}}} $\end{document}</tex-math></inline-formula> 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.</p><p style='text-indent:20px;'> </p><p style='text-indent:20px;'>Erratum: The name of the fifth author has been corrected from Jussi Toivainen to Jussi Toivanen. We apologize for any inconvenience this may cause.</p>