## 3 Results and Analyses
### The Quality Evaluation of Photoacoustic Image  
The performance of the proposed method is further verified by evaluating the quality of photoacoustic images. The photoacoustic image obtained by the proposed method is compared with the images obtained based on a homogeneous sound speed field and the k-means sound speed estimation method. Figure 14 gathers the real digital breast model and the photoacoustic images obtained by the above three sound speed estimation methods. As shown in Figure 14b, there are many artifacts in the photoacoustic image obtained based on the homogeneous sound speed field, and the boundaries of each tissue are blurred. The shape of the tumor tissue is distorted and the position of the skin tissue is obviously deviated. Figure 14c shows the photoacoustic image obtained based on the k-means sound speed estimation method. The artifacts of this image are reduced and the shape of the tumor tissue is closer to a real tumor shape. However, the sharpness of the image is still poor, and many details of the model are not shown. The photoacoustic image obtained by the proposed method is shown in Figure 14d. Compared with the photoacoustic images obtained by the other two methods, the sharpness of this image is significantly improved. Not only is the position of each tissue accurately located, but also, the details in the image are very clear. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Coupling Medium and Biological Tissues**} & **Real Sound** & \multicolumn{2}{c}{**Initial Sound Speed (m/s)**} & \multicolumn{2}{c}{**Optimal Sound Speed (m/s)**} \\ \cline{2-5}  & **Sound Speed** & \(\Delta v_{1}\) & **Sound Speed** & \(\Delta v_{2}\) \\ \hline water & 1500.00 & 1500.00 & 0.00 & 1500.00 & 0.00 \\ fibrogland & 1515.00 & 1495.00 & \(-\)20.00 & 1510.62 & \(-\)4.38 \\ fat & 1440.00 & 1495.00 & 55.00 & 1440.68 & 0.68 \\ skin & 1540.00 & 1495.00 & \(-\)45.00 & 1537.98 & \(-\)2.02 \\ tumor & 1470.00 & 1495.00 & 25.00 & 1470.50 & 0.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The absolute error of the sound speed of each tissue in the initial and optimal sound speed fields relative to the real sound speed. The quality of the photoacoustic image is quantitatively evaluated by the photoacoustic pressure amplitude error map. In Figure 14, the photoacoustic pressure amplitude marked by white dashed lines in the four images is extracted for error analysis. The absolute error of the photoacoustic pressure amplitude of the three sound speed estimation methods relative to the true amplitude is shown in Figure 15. In this figure, gray dotted line boxes are used to identify the three parts with the most obvious contrast of errors. Dotted line boxes 1 and 2 indicate skin, and dotted line box 3 indicates tumor 2. Through observing these three parts, it can be seen that the amplitude error of the homogeneous sound speed field and k-means sound speed estimation method is significantly larger than the error of the proposed method. The comparison results of absolute error show that the photoacoustic image obtained by the proposed method has higher fidelity. Figure 14: Digital breast model and photoacoustic images obtained by three sound speed estimation methods. (**a**) Digital breast model. (**b**) Photoacoustic image obtained by homogeneous sound speed. (**c**) Photoacoustic image obtained by the k-means sound speed estimation method. (**d**) Photoacoustic image obtained by the proposed method. Figure 15: Absolute error of photoacoustic pressure amplitude for the three sound speed estimation methods. The quality of the photoacoustic image obtained based on the proposed method is quantitatively analyzed by the commonly used image evaluation index. The peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) of the photoacoustic images obtained by the above three methods are calculated. Among them, the PSNR is used to measure the difference between the reconstructed image and the original image.