## 3 Results
The ultimate purpose of obtaining the envelope signal is to determine a suitable inhibitory factor, so even if the amplitude of the envelope signal obtained after multiplied by the window function is greatly changed compared with the previous, it will not have much impact on the final imaging results. In order not to alter the amplitude, we still choose to use the data corresponding to the moment \(t_{0}=0\) of the original envelope signal as the initial imaging data. Then, the final output result of the method we propose is as follows:  
\[Y_{w-inv}=Env(x,y;t_{0})\times inv^{k}(x,y;t_{0}), \tag{13}\]  
the definition of the inhibitory factor is as follows:  
\[inv(x,y;t)=\frac{Env_{win}(x,y;t)}{Env_{win}\left(x,y;t_{peak}\right)}, \tag{14}\]  
where \(Env_{win}(x,y;t)\) refers to the envelope signal obtained after combining the window function, the calculation method and formula of \(t_{peak}\) are the same as those in Equation (8). The value of \(k\) is set at 3 based on the established criteria discussed earlier. Therefore, when imaging again, the reconstruction result will not have the distortion problem caused by overshoot. To facilitate a visual comparison, we have integrated the reconstruction results obtained using four different methods into one figure, as shown in Figure 10.  
The DAS algorithm, which merely calculates the initial values of signals during the imaging process, leads to prominent artifacts in the reconstructed images. Additionally, there exists a certain degree of deviation in the shape of the reconstructed sources as shown in Figure 10a. The results obtained by using the DMAS method for reconstruction have reduced artifacts, but the reconstructed images have obvious discontinuities and distortions in shape, which is shown in Figure 10b. Compared with DAS, the multi-DASE algorithm shows significant improvement and effectively reduces the presence of artifacts. Figure 9: The envelope signal without window and envelope signal multiplied by the window function at the center of a circular source with a radius of 1.5 mm. However, it has the problem of internal structure omission caused by the overshoot of the envelope signal, as shown in Figure 10c. The method we proposed not only ensures that the artifacts are suppressed, but also retains the internal information of the source more comprehensively, as shown in Figure 10d. We calculated the Structural Similarity Index (SSIM) of the reconstructed images obtained using the DAS algorithm, the multi-DASE algorithm, and our proposed method to quantify the superiority of our proposed method. The SSIM has a good correlation with human subjective visual perception and can intuitively reflect the effectiveness of the reconstructed images through the data. Before calculating the SSIM, we need to normalize the reconstructed images obtained by different methods. The data are presented in Table 1.  
The table above presents the SSIM values calculated by comparing the reconstruction results from different methods with the initial sound pressure field. The DAS algorithm simply sums the data for imaging, and the reconstructed image has a lot of artifacts, and there are negative values in the reconstructed data, so its SSIM value is very low, it is just 0.0187. The DMAS method can suppress artifacts and the SSIM value has been improved to 0.5486. However, due to the problems of slice and shape distortion, there is still much room for improvement. Although the DASE algorithm suppresses the artifacts to a large extent, its source is also suppressed, so its SSIM value is improved compared with the \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **DAS** & **DMAS** & **DASE** & **Proposed Method** \\ \hline SSIM & 0.0187 & 0.5486 & 0.7518 & 0.8660 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: SSIM for circular source using various methods. Figure 10: Imaging results obtained by various methods.