## 3 Results
(**a**) Reconstructed image using DAS; (**b**) reconstructed image using DMAS; (**c**) reconstructed image using multi-DASE; (**d**) reconstructed image using proposed method. former two methods, reaching 0.7518, but there is still a lot of room for improvement. The reconstructed image obtained by our method can suppress the artifacts and distinguish the source at the same time, so it is most similar to the original sound source field, and the SSIM index reaches 0.8660. We extracted the lateral profile at \(y=10.8\) mm and the vertical profile at x = 10.8 mm, respectively, of the reconstructed image using the DASE algorithm and the method proposed in this paper. Figure 11a,c show the lateral profile and vertical profile at the center of the circle source of the reconstruction imaging using multi-DASE, and they show that there is clearly inhibition within the source. Figure 11b,d are the lateral profile and vertical profile at the center of the circle source of the reconstruction imaging using the method proposed in this paper, and show that there are no obvious faults in the reconstructed images processed by our method. The signal distribution within the sound source is more uniform, no abnormal suppression phenomenon occurs, the overall signal strength remains good, and there is no obvious signal loss. Although this section focuses solely on presenting the reconstruction results of a sound source with a radius of 1.5 mm using various methods, as previously discussed, our approach can adaptively adjust the Gaussian window size based on the sound source dimensions. So our method is applicable to sound sources of different sizes. To verify the robustness of our method under different noise levels, we added random Gaussian white noise of different levels for simulation. Figure 12 shows the reconstructed images at different noise levels. Figure 12a shows the reconstruction results obtained using  
Figure 11: Profile for different methods. **(a,b)** Lateral profile at \(y=10.8\) mm for DASE and proposed method. **(c,d)** Vertical profile at x = 10.8 mm for DASE and proposed method. different methods when the SNR ratio is 34 dB. The noise level is relatively low, and the reconstruction result is not very different from that in the noise-free case. Figure 12b shows the reconstruction results obtained using different methods when the SNR ratio is 20 dB. It can be seen that the reconstructed images obtained by the four methods are all affected by noise, resulting in a decrease in reconstruction quality. Figure 12c shows the reconstructed images obtained using different methods when the signal-to-noise ratio is 17 dB. Due to the high noise level, the reconstruction results obtained by various methods have all been affected. To quantitatively compare the robustness of different methods in dealing with noise, we calculated their respective SSIM values for comparison, and the results are shown in Table 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**SNR** & **DAS** & **DMAS** & **DASE** & **Proposed Method** \\ \hline
**34 dB** & 0.0185 & 0.5173 & 0.7360 & 0.8602 \\
**20 dB** & 0.0168 & 0.4908 & 0.6980 & 0.8328 \\
**17 dB** & 0.0167 & 0.3625 & 0.6105 & 0.8164 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: SSIM of various methods at different SNRs. Figure 12: Imaging results obtained by various methods at different noise levels. (**a**) The SNR is 34 dB; (**b**) the SNR is 20 dB; (**c**) the SNR is 17 dB. The data shown in Table 2 can demonstrate that, under different noise levels, the quality of the reconstructed images obtained by our proposed method remains the highest. Additionally, as the noise level increases, the SSIM of the reconstruction results of the DMAS method decreases by 0.1548, that of the DASE method decreases by 0.1255, and that of our method decreases by 0.0442, verifying the robustness of our method.