## 3 Results and Analyses
### The Error Analysis of Sound Speed  
The accuracy of the inhomogeneous sound speed field is further evaluated from the angle of sound speed error. The sound speeds of various tissues are extracted from the real, initial and optimal sound speed fields. The absolute error of the sound speed of each tissue in the initial and optimal inhomogeneous sound speed fields relative to the real sound speed is calculated. As shown in Table 3, \(\Delta v_{1}\) represents the absolute error between  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**Proposed Method**} & \multirow{2}{*}{**K-Means Method**} \\ \cline{2-3} \cline{5-5}  & **Initial Clustering Result** & & **Optimal Clustering Result** \\ \hline SSE & 2.1497 \(\times\) 10\({}^{7}\) & 9.0447 \(\times\) 10\({}^{6}\) & 4.7271 \(\times\) 10\({}^{7}\) \\ SP & 0.1817 & 0.2697 & 0.1955 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The SSE values and SP values of the clustering results obtained by the proposed method and the k-means sound speed estimation method.  
the sound speed of each tissue in the initial sound speed field and the real sound speed. \(\Delta v_{2}\) represents the absolute error between the sound speed of each tissue in the optimal sound speed field and the real sound speed. Comparing the absolute error in Table 3, it can be seen that the absolute values of the \(\Delta v_{2}\) of various tissues are much smaller than the absolute value of \(\Delta v_{1}\). These indicate that the sound speeds of various tissues in the optimal sound speed field are closer to the real sound speed. The proposed method can significantly improve the accuracy of the sound speed of each tissue.  
The sound speed field obtained by the k-means sound speed estimation method is assigned according to the real sound speed values in Table 1. However, the sound speeds in the optimal sound speed field obtained by the proposed method still have small errors with the true sound speed values. Therefore, only from the angle of sound speed error, the accuracy of the sound speed of each tissue obtained by the proposed method is slightly worse than that of the k-means sound speed estimation method.  
The above evaluation results show that the proposed method can significantly improve the accuracy of the inhomogeneous sound speed field from the two perspectives of clustering results and sound speed errors. In addition, the comparison results with the k-means sound speed estimation method show that the proposed method has better clustering performance. The region distribution of each tissue in the optimal sound speed field obtained by this method is more accurate. However, the sound speed error of each tissue is not completely eliminated, and the accuracy of the sound speed value is slightly worse than that of the k-means estimation method. In this case, the sound speed field obtained by the two methods is unable to accurately judge which one has better quality. The photoacoustic images based on these two sound speed fields need to be evaluated to further prove whether the sound speed field obtained by the proposed method is more accurate.