## 3 Numerical Implementation
### Evaluation of the Reconstructions  
The fusion of D-Bar and EIT data with the D-Bar algorithm introduces a variety of hyperparameters that all affect the quality of the reconstruction. The standard D-Bar method has the truncation radius \(R_{1}\) as a hyperparameter. In our approach, a second truncation radius is introduced, which is similar to [35]. As mentioned in Section 3.5, the _a priori_ conductivity \(\sigma_{prior}\) also has an effect on the reconstruction. Finally, the effect of noise on the reconstruction is of great interest, as the radar data might be able to make the algorithm more robust to noise. We use the GREIT figures of merit for the evaluation of the reconstructions [36]. These performance metrics are well established for the evaluation of different reconstruction algorithms in EIT. The data have to be preprocessed to use the GREIT figures of merit in a D-Bar setting, as the GREIT figures of merit assume that the reconstruction background is centered around 0, which is the case for the majority of time-differential EIT algorithms, such as GREIT, Gauss-Newton, or NOSER. The D-Bar reconstructions are centered around 1; thus, impedance inclusions with a conductivity greater than the background are greater than one, and conductivities smaller than the background are smaller than one, but still above zero. We simply subtract 1 from the reconstructed impedance values to apply the  
Figure 7: Visualization of the merging in the k-space. The purple area represents the k-space that is filled with \(\mathbf{t}^{radar}(k)\), while the red area is filled with \(\mathbf{t}^{EIT}(k)\). Values outside \(|k|<=R_{2}\) are zero. GREIT figures of merit, as this allows us to use the standard GREIT figures of merit. The figures of merit are as follows:  
Firstly, the quarter-amplitude set \(\mathbf{x}_{q}\) is calculated, which is defined as  
\[\widehat{\mathbf{x}}_{q}\,=\, \begin{cases}1&[\mathbf{x}]_{i}\geq\frac{1}{4}max(\mathbf{x}) \\ 0&\text{otherwise}\end{cases} , \tag{24}\]  
where \([\mathbf{x}]_{i}\) is each pixel in the reconstructed image. According to [PERSON] [36], the value of the threshold is somewhat arbitrary and has little effect on the results. Amplitude response (**AR**) is the summation of all pixels in the quarter-amplitude set divided by the sum of all pixels in the reference image. It is calculated as follows:  
\[\textbf{AR}=\frac{\sum\widehat{\mathbf{x}}_{q}}{\sum\mathbf{x}_{0}}, \tag{25}\]  
where \(\mathbf{x}_{0}\) is the impedance target pixels of the reference image. The **AR** should be close to 1. The position error (**PE**) measures the distance from the center of gravity (\(cog\)) of the true conductivity to that of the reconstructed conductivity. Here, we differ slightly from the original definition as our domain is not symmetric; however, the general idea is still the same. We define the **PE** as  
\[\textbf{PE}=\sqrt{(cog_{x}^{o}-\widehat{cog}_{x})^{2}+(cog_{y}^{o}-\widehat{cog }_{y})^{2}}, \tag{26}\]  
where \(cog_{i}^{o}\,i\in[1,2]\) is the \(i^{th}\) component of the center of gravity of the true conductivity distribution and \(\widehat{cog}_{i}\,i\in[1,2]\) is the \(i^{th}\) component of the center of gravity of the reconstructed quarter-amplitude-set conductivity. The **PE** should be as small as possible. The reconstruction resolution (**RES**) measures the fraction of the area of the quarter-amplitude set to the area of the entire medium. It is calculated as  
\[\textbf{RES}=\sqrt{\frac{A_{q}}{A_{0}}}, \tag{27}\]  
where \(A_{q}\) is defined as the area of the quarter-amplitude set and \(A_{0}\) is defined as the area of the entire medium. The **RES** should be low, as this allows one to distinguish impedance enclosures better. The shape deformation (**SD**) measures the fraction of the quarter-amplitude set which does not fit into an equal-sized circle area.