## 4 Results
### Measurement Data  
For validation the neural network, trained on synthetic data, was employed on experimental data. The measurements, shown here, were performed at the resonance frequency of the Helmholtz resonators at \(f_{R}=1479\) Hz. Some resonators were deactivated by filling resonator volume with liquid, to avoid a hexagonal rotational symmetry. The first row of Figure 11 shows the sinograms with the full scanning angle (a), limited scanning angle (b) and the neuronal network based extrapolation (c). To get the limited angle sinogram, the outer angles in the scan range [0, 40]\({}^{\circ}\) as well as [140, 180]\({}^{\circ}\) were removed. The second row shows corresponding filtered back projection of the sinograms (d-f). The bottom row describes the relative error referred to the full angle filtered back projection tomographic reconstruction. The local error for limited angle and neural network reconstruction are depicted in (h,i). Boxplots at (g), show the corresponding  
Figure 10: Limited angle and neural network extrapolated error distribution of tomographic reconstruction in dependency of model complexity. error distribution. In addition, the location of the active resonators were marked in each case in the reconstruction. In Figure 11, artifacts due to stitching the measurements can be seen. This results in horizontal lines in the sinograms (a-c) and circles in the reconstructions (d-f). Furthermore, strong distortions for radii above 45 mm due to the optical aberrations induced from the glass cylinder are apparent. In the full angle reconstruction (d), a reduction of the sound pressure by 0.4 Pa can be seen above each active resonator. The resonators have a circular contour. The deactivated resonators can also be seen clearly. There is no characteristic minimum in the area above  
Figure 11: Measured sound pressure field reconstruction: (**a**) full angle (FA) sinogram; (**b**) limited angle (LA) sinogram; (**c**) neural network (NN) extrapolated sinogram; (**d**) full angle filtered back projection tomographic reconstruction; (**e**) limited angle filtered back projection tomographic reconstruction; (**f**) neural network extrapolated filtered back projection tomographic reconstruction; (**g**) error distribution of local reconstructions compared to full angle reconstruction; (**h**) local error of limited angle reconstruction compared to full angle reconstruction; (**i**) local error of neural network reconstruction compared to full angle reconstruction. the resonator. That means this area has no local acoustic damping effect. The limited angle reconstruction (e) shows similar artifacts to the reconstruction of synthetic data, additionally to the measurement artifacts, mentioned in the full angle reconstruction. Line artifacts, as well as amplitude errors, are present. The contours of the resonators are elliptical. The amplitude over the resonators reconstructed with limited angle deviates by 0.23 Pa compared to the full angle reconstruction. The sinogram of the neural network extrapolated data (c) shows a hard transition from the extrapolated angular scan range. There is a spatial low-pass effect in the extrapolation. However, this reconstruction (f) also shows a significant improvement compared to the limited angle reconstruction. The contour of the resonator is round and artifacts are strongly attenuated. The amplitude over the resonators reconstructed with neural network extrapolation deviates by 0.05 Pa compared to the full angle reconstruction. The comparison of the limited angle and neural network with the full angle reconstruction shows that, overall, a significant reduction in relative error distribution can be achieved with the neural network extrapolated sinogram. Especially, in a close range around the Plexiglas wall an error reduction with neural network reconstruction is noticeable. Local errors surrounding the position of local resonators, are present in Figure 11h. This means every hole has a significant local sound pressure error compared to the full angle reconstruction.