# Photoacoustic Imaging with a Finite-Size Circular Integrating Detector
## 4 Test and Discussion
### Comparison with Wiener Deconvolution  
The method proposed in this study was compared with Wiener deconvolution, and the results demonstrate that the proposed approach is more effective in reducing blur and enhancing image edge details. Figure 8a shows the blurred image. Although the general shape of the blood vessels is visible, the image suffers from edge blurring and unclear details. Figure 8b shows the results after Wiener deconvolution, where the blur is somewhat reduced. However, due to the limitations of Wiener deconvolution in processing high-frequency image details, especially its tendency to confuse edges and details with noise during the estimation process, the edges and details of the image are excessively smoothed, making it impossible to preserve the original features accurately. As a result, as shown in Figure 8b, the edges of the blood vessels remain unclear. Figure 8c presents the image processed using the proposed method, where significant improvements in edge sharpness, a noticeable reduction in artifacts, and more precise blood vessel details can be observed.  
Figure 9 illustrates a comparison of the blurred pressure distribution profile \(p_{j}^{\theta}(\phi)\), the pressure distribution profile \(p_{j}^{0}(\phi)\) calculated using the proposed algorithm, and the one  
Figure 8: (**a**) Blurred image; (**b**) Wiener deconvolution processed image; (**c**) the image processed using the algorithm proposed in this article.  
Figure 7: (**a**–**d**) represents the relative sizes of 531 feature values corresponding to 3 \(p_{j}^{\theta}(\phi)\) data inputs. After recalculating the feature values, the relative sizes of 25 feature values are obtained, CPD, \(h_{\theta}(\phi)\), represented in blue. (**e**–**h**) represents the relative sizes of 531 feature values corresponding to four \(p_{j}^{\theta}(\phi)\) data inputs. After recalculating the feature values, the relative sizes of 25 feature values are obtained, CPD, \(h_{\theta}(\phi)\), represented in red.  
\(p_{j}^{W}(\phi)\) calculated using the Wiener deconvolution algorithm (\(j=57\)). As shown, the polar pressure distribution profile in Figure 9a appears relatively \"smooth\", lacking the delicate and sharp details commonly observed in accurate reconstructions, and it exhibits an overall blurred and smooth appearance. The profile processed by the Wiener deconvolution algorithm (Figure 9b) demonstrates clearer and sharper features but is accompanied by noticeable fluctuations, i.e., noise, which negatively affects the overall quality. In contrast, the profile obtained using the proposed algorithm (Figure 9c) excels in detail recovery, especially in reconstructing edge features and delicate structures, and it aligns more closely with the original assumed initial pressure distribution profile.  
Table 2 presents the quantitative evaluation results using the PSNR and SSIM metrics to compare the image quality under different processing methods.  
The blurred image had a PSNR of 10.41 dB and an SSIM of 0.6245. The Wiener deconvolution method improves the image quality with a PSNR of 23.26 dB and an SSIM of 0.7866, but the proposed method outperforms it, achieving a PSNR of 32.09 dB and an SSIM of 0.9823. This indicates a significant enhancement in image quality, particularly in recovering fine details and edge features, with PSNR improving by 8.83 dB and SSIM increasing by 0.1957 compared to the Wiener deconvolution results. Overall, the proposed method significantly improves the clarity and accuracy of photoacoustic images, particularly in high-resolution imaging tasks. Compared to the Wiener deconvolution algorithm, it demonstrates superior performance in recovering image details and edge features.