## 4 Results  
### Synthetic Data  
A synthetic sound pressure field was generated according to the parameters presented in Table 1 (2. line). The first row of Figure 9 shows the sinograms with full scanning angle (a), limited scanning angle (LA) (b) and the neuronal network based extrapolation (c). The second row shows corresponding local data computed by filtered back projection (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 error distribution. The modeled constant sound pressure field in the cylinder (Figure 9i)) results in a quadratic function in the sinogram over the projection axis. In the angular axis, the function is constant. Each hole produces a reduction in the total amplitude on each measurement in the angular scan range. If several resonators are in succession in the direction of projection, the reduction in amplitude is summed. The hole position has a sinusoidal curve over the scanned angle axis. These correlations were learned without the possibility of mirroring or repeating certain parts of the already given range by training the neural network. It can be seen that a reconstruction using filtered back projection of the measurement data with full angular scan range leads to an artifact-free reconstruction result, only higher noise emissions are visible. On the contrary, when reconstructing with a limited angular scan range, clear artifacts can be seen. Individual resonators have an elliptical shape and become blurred. This leads to an inseparability of individual resonators if they are close to each other. Furthermore, an incorrect absolute value reconstruction occurs, which deviates both downwards and upwards. Locally, especially between neighboring resonators, excessive sound pressure values are reconstructed and the values within a hole are calculated as too low. The sinogram extrapolated by means of neural network shows a considerable qualitative improvement in the reconstruction. The resonators regain their circular shape and are separable. However, a low-pass effect can be seen at the hole edges in the extrapolated angular regions. For a quantitative comparison between limited angle reconstruction and neural network reconstruction, the relative local deviation towards the full angle reconstruction was calculated and is presented in Figure 9h,i. In the comparison of the two reconstructions, a clear reduction of the relative error for the neural network reconstruction can be seen. Large areas of the limited angle reconstruction have an error above 10% whereas the error of the neural network reconstruction is larger than 10% only in the area of large hole clusters. In the region of hole accumulations there are high spatial frequencies due to edges. However, when extrapolating the missing angular regions, there is a spatial low-pass effect. Thus, the high spatial frequencies are missing in the sinogram. The filtered back projection additionally attenuates low spatial frequencies. This amplifies the noise in the entire loose sound field. Especially in the area of high spatial frequencies, this leads to an incorrect reconstruction. For better comparability of the overall results, the distribution of the magnitude relative error over the middle part of the sound field in the area (35 mm \(\times\) 35 mm) was calculated and is shown in Figure 9g. This avoids a distortion of the comparison due to edge effects. It can be seen that the error of the reconstruction using neural network was significantly reduced from mean value 9.8% to 4.6% compared to the reconstruction without extrapolation. Especially the maximum error could be reduced by more than 10%. With this approach an enhancement of local reconstruction results by a factor of 2 can be reached at an limited angular scan range of \([40,140]^{\circ}\).