with $\operatorname{M^{\mbox{\tiny{\textbf{exp}}}}}(z,0)$, using a numerical derivative such as centered finite-differences, and the admittivity obtained via convolutions and two-dimensional [FFT]{}s $$\begin{aligned}
\operatorname{\gamma^{\mbox{\tiny{\textbf{exp}}}}}(z) &=& \exp\left\{-2h_z^2\;IFFT\left[FFT\left(\frac{1}{\pi \bar{z}}\right)\;FFT(\operatorname{Q_{12}^{\mbox{\tiny{\textbf{exp}}}}})\right]\right\}\\
&=& \exp\left\{-2h_z^2\;IFFT\left[FFT\left(\frac{1}{\pi {z}}\right)\;FFT(\operatorname{Q_{21}^{\mbox{\tiny{\textbf{exp}}}}})\right]\right\}\end{aligned}$$ where $h_z$ denotes the uniform step size in the $z$ grid, and again we have used the fundamental solutions for $\operatorname{\operatorname{\partial}_z}$ and $\operatorname{{\bar{\partial}}_z}$, respectively. If the DN matrix $\mathbf{L}_\gamma$ was scaled by $\gamma_0\neq 1$, then undo the scaling now by multiplying by $\gamma_0$.

[[Evaluation methods]{}]{} {#sec:eval_mtds}
--------------------------

The robustness of the D-bar methods are demonstrated on EIT data from the [ACT3]{} and [ACT4]{} EIT systems of Rensselaer Polytechnic Institute (RPI) \[[@Cook1994; @Liu2005]\] and the [ACE1]{} EIT system of Colorado State University (CSU) \[[@MellenthinEMBS_2015]\]. See Figure \[fig:phantoms\] for the experimental setups.

(320,130) (0,0)[![Experimental setups for test phantoms from the ACT3, ACT4, and ACE1 EIT systems.[]{data-label="fig:phantoms"}](TankSetup_clipped_DICOM.png "fig:"){width="90pt"}]{} (100,0)[![Experimental setups for test phantoms from the ACT3, ACT4, and ACE1 EIT systems.[]{data-label="fig:phantoms"}](H2L_saline_clipped_small.jpg "fig:"){width="90pt"}]{}

(200,0)[![Experimental setups for test phantoms from the ACT3, ACT4, and ACE1 EIT systems.[]{data-label="fig:phantoms"}](ACE1_ChestTankPic_AgarHnL_trimmed.PNG "fig:"){width="120pt"}]{}

(25,105) (15,95)

(130,105) (115,95)

(245,105) (220,95)

The ACT3/ACT4 data were collected on a saline-filled tank of radius 15 cm with 32 electrodes of width 2.5 cm on the boundary. The ACT3 data set is archival, with an agar heart (0.75 