# A NEW ALTERNATIVE ELLIPTIC PDE IN EIT IMAGING

• Kim, Sungwhan
• Published : 2012.11.30
• 51 3

#### Abstract

In this paper, we introduce a new elliptic PDE: $$\{{\nabla}{\cdot}$\frac{|{\gamma}^{\omega}(r)|^2}{\sigma}{\nabla}v_{\omega}(r)$=0,\;r{\in}{\Omega},\\v_{\omega}(r)=f(r),\;r{\in}{\partial}{\Omega},$$ where ${\gamma}^{\omega}={\sigma}+i{\omega}{\epsilon}$ is the admittivity distribution of the conducting material ${\Omega}$ and it is shown that the introduced elliptic PDE can replace the standard elliptic PDE with conductivity coefficient in EIT imaging. Indeed, letting $v_0$ be the solution to the standard elliptic PDE with conductivity coefficient, the solution $v_{\omega}$ is quite close to the solution $v_0$ and can show spectroscopic properties of the conducting object ${\Omega}$ unlike $v_0$. In particular, the potential $v_{\omega}$ can be used in detecting a thin low-conducting anomaly located in ${\Omega}$ since the spectroscopic change of the Neumann data of $v_{\omega}$ is inversely proportional to thickness of the thin anomaly.

#### Keywords

electrical impedance tomography;alternative elliptic PDE;spectroscopic change;anomaly thickness

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#### Acknowledgement

Supported by : Korea Research Foundation