## 3 Results
### Imaging Performance with Limited Data
#### 3.2.2 Reconstructions of Small Target at an Offset Height Using a Headband  
We consider another scenario in which a small target is placed in-between a two-ring array surrounding the model of Figure 2. The head phantom comprises white matter and includes a target at the same \(x\)-\(y\) position as previously, but with a smaller radius \(\rho=10\) mm and height \(h=20\) mm for the WT case. As the immersion liquid cannot extend infinitely in a practical scenario, we consider a headband of finite dimensions filled with the immersion liquid and surrounded by air. The setup is shown in Figure 14. The two rings are placed with an offset in the x-y plane, to obtain information from more angles and reduce coupling. The target covers an area between the x-\(y\) planes of the two rings only, as shown in Figure 14a. We have considered different ways of applying our 2-D imaging algorithm to the data by the two-ring array by using: (1) the bottom ring data, (2) the top ring data, and (3) combined data from both rings as if they were on the same plane, effectively creating a sixteen-antenna array for the slice reconstructed in 2-D, which was selected as the slice of the target center. The head model for the cases considered in this subsection (Cases III.1, 2 and 3) is shown in Figure 15, while the headband used in each case is different. We note that the \"homogeneous white-matter\" head model of Figure 15 is unrealistic, but it was selected to focus on comparing 3-D with 2-D results of more realistic arrays and smaller targets. To compare the errors of the target domain more clearly, we have also defined an \(RMSE\) in the selected target slice as \(RMSE\)-\(T\). \"Case III.1\" considers a headband of \(\rho=130\) mm radius and \(h=110\) mm height filled with the glycerol-water mixture. The antennas are very close to the air-liquid interface in all directions (top/bottom/side) for this case, resulting in strong reflections from the interface. The reflections can be taken into account by our 3-D FDTD model along all dimensions, while the 2-D model can only model the x-y boundary. In both models, of course, the wave reflections from the boundary will be different for the realistic CST model relative to its  
Figure 14: (**a**) Top and (**b,c**) side views of the setup used in Section 3.2. A headband is placed at the top of the head phantom, and sixteen antennas are placed in a two ring array inside the headband, with 8 antennas for each ring. Figure 13: 2-D reconstructions of \(\Re(\varepsilon_{r})\) at 1.0 GHz: (**a**) Case II.1, and (**b**) Case II.2. A cylindrical eight-antenna array centered at the target height is used to produce the data. simplified version in FDTD, firstly because realistic antennas have been replaced by simple point sources. Results from 3-D and 2-D reconstructions are shown in Figure 16.  
Despite including the interface in the 3-D model, the reconstructed images suffer from strong artifacts near the interface, which suggest that the mismatch between the CST and FDTD model is significant. The target is reconstructed to some extent, but it is difficult to detect it with certainty. The 2-D reconstructions fail to detect the target completely regardless of whether we use data from the top, bottom, or both rings. This is not surprising given that the target is not aligned with any of these rings, and that the interface between air and the glycerol-water immersion liquid cannot be fully modeled in 2-D.  
To examine the impact of this interface and improve detection performance, \"Case III.2\" considers the same headband as Case III.1, which is now surrounded by an additional layer of absorbing material. The headband layers are as follows: glycerol-water mixture, plastic, absorbing material (ECCOSORB MCS), and a metallic shield. Finally, \"Case III.3\" uses a a larger size (\(\rho=140\) mm and \(h=120\) mm) headband with the same materials as Case III.1. As with the absorbers in Case III.2, increasing the distance between the antennas and the interface with air can reduce the resulting reflections.