• Toivanen, Jussi

Abstract

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

Topics

• impedance spectroscopy
• positron annihilation lifetime spectroscopy
• Photoacoustic spectroscopy