data directly in terms of the DN map $\Lambda_{\gamma}$ \[[@Herrera2015]\]: $$\label{eq:Fran_scatNata}
\begin{array}{lcl}
S_{12}(k) & =& \frac{i}{4\pi}\int_{\partial\Omega} e^{-i\bar{k}z}\left(\Lambda_{\gamma}+i\partial_{\tau}\right)u_2(z,k)\;ds(z)\\
S_{21}(k) & =& -\frac{i}{4\pi}\int_{\partial\Omega} e^{i\bar{k}\bar{z}}\left(\Lambda_{\gamma}-i\partial_{\tau}\right)u_1(z,k)\;ds(z),
\end{array}$$ where $\partial\tau$ denotes the tangential derivative operator: $\partial_\tau f(z) = \nabla f(z) \cdot \tau$. Again, using the asymptotic behavior of the CGO solutions $u_1$ and $u_2$ gives a [*Born approximation*]{} to the scattering data $$\label{eq:Fran_scatExp}
\begin{array}{lcl}
\operatorname{S_{12}^{\mbox{\tiny{\textbf{exp}}}}}(k) & =& \frac{i}{4\pi}\int_{\partial\Omega} e^{-i\bar{k}z}\left(\Lambda_{\gamma}+i\partial_{\tau}\right)\left(\frac{e^{-ik\bar{z}}}{-ik}\right)ds(z)\\
\operatorname{S_{21}^{\mbox{\tiny{\textbf{exp}}}}}(k) & =& -\frac{i}{4\pi}\int_{\partial\Omega} e^{i\bar{k}\bar{z}}\left(\Lambda_{\gamma}-i\partial_{\tau}\right)\left(\frac{e^{ikz}}{ik}\right)ds(z),
\end{array}$$

The reconstruction process is then:

1.  Given $\Lambda_\gamma$, compute the [*Born*]{} scattering data for $\left\{\operatorname{S_{12}^{\mbox{\tiny{\textbf{exp}}}}}(k),\;\operatorname{S_{21}^{\mbox{\tiny{\textbf{exp}}}}}(k)\right\}$ from , for $0<|k|\leq R$ for some chosen radius $R$.

2.  Solve the $\operatorname{{\bar{\partial}}_k}$ equation , using $\operatorname{S^{\mbox{\tiny{\textbf{exp}}}}}(k)$, for each $z\in\Omega$.

3.  Recover the admittivity $\gamma^{\mbox{\tiny{exp}}}$ using the matrix potential $Q^{\mbox{\tiny{exp}}}$ .

Note that [*‘Approach 2’*]{} does not require the DN map $\Lambda_1$ and thus no simulation of data is needed to obtain absolute images. Aside from Calderón’s original method \[[@Calderon1980], [@Bikowski2008], [@Muller2017]\], this is the only method for absolute imaging of EIT that does not need any simulated data. This has the key benefits of not needing to know the locations of electrodes with high precision, contact impedances at the electrodes, or even near perfect knowledge of the boundary shape. As we demonstrate below 