## 4 Results and Discussion
### De-Blurring Image
These models were trained using a carefully curated input and output image pairs dataset. A combination of PSF convolutions at different depths was used to train the Attention U-Net and Attention Res-UNet networks for image de-blurring. This involved pairing the original images with their corresponding blurred counterparts. This approach enabled the networks to learn the intricate relationships between different depths and their corresponding blurred representations, facilitating accurate image de-blurring. In the statistics table of the Dice coefficient for the two models, Attention Unet and Attention Res-UNet, as shown in Table 3, we can observe crucial information on the performance of these models. The Attention Unet model achieved a minimum Dice coefficient of 0.931 and a maximum of 0.999487, with a mean of 0.996319 and a median of 0.999195. The variability in the performance of this model is represented by a standard deviation of 0.009583. Similarly, the Attention Res-UNet model exhibits comparable parameters, with a minimum Dice coefficient of 0.930391 and a maximum of 0.999492. The mean and median values for this model are 0.996443 and 0.999223, respectively. The performance variability of the Attention Res-UNet model is gauged by a standard deviation of 0.009603. Overall, both models demonstrate consistent performance with minimal variation across the Dice coefficient values. This underscores the efficiency and general applicability of the models in de-blurring absorption structures within a dispersed medium. Figure 9 provides a visual representation of the process. Figure 10 illustrates a representative example of input and output images obtained by scatter blurring at various depths, specifically 0.1, 5.0, 10.0, and 20.0 mm. In particular, the corresponding correlation indices for these depths were reported as 0.9360, 0.9167, 0.9130, and 0.9059, respectively. These correlation indices served as valuable quantitative indicators, providing insights into the level of agreement between the predicted de-blurred output and the ground truth images. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **Minimum** & **Maximum** & **Mean** & **Median** & **Std** \\ \hline Attention Unet & 0.931056 & 0.999487 & 0.996319 & 0.999195 & 0.009583 \\ Attention Res-UNet & 0.930391 & 0.999492 & 0.996443 & 0.999223 & 0.009603 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance Comparison of Attention Unet and Attention Res-UNet Models based on Dice Coefficient Statistics. Figure 8: Scattering de-blurring with and without residual block: (**A**) transillumination image through turbid medium, (**B**) image taken through clear water, (**C**) output image from U-Net model, and (**D**) output image from Residual Unet model. Figure 9: Training and validation for de-blurring process: (**A**,**B**) Attention U-Net, (**C**,**D**) Attention ResNet UNet. Figure 11 illustrates the original and restored images of the absorbing structure after applying the Attention U-Net and Attention Res-UNet models. Then, the correlation coefficient is calculated. As the depth of the absorbing structure increases, the blurring effect becomes more pronounced, leading to a rapid decline in the quality of the blurred image. Furthermore, the reduction in training images significantly affects the correlation coefficient. Figure 11: Correlation analysis between original and deblurred images with \(256\times 256\) input image size. Figure 10: Representative images demonstrating the de-blurring process at various depths: (**A**) 0.1 mm, (**B**) 5 mm, (**C**) 10 mm, and (**D**) 20 mm. The test results for the Attention U-Net model indicated that the correlation coefficient exhibited a high value ranging from 0.9149 to 0.9013 for depths between 0.1 and 5.0 mm. Beyond 5.0 mm, the correlation coefficient gradually decreased, reaching 0.8921 at a depth of 10.0 mm. Subsequently, for depths ranging from 10.1 to 20.0 mm, the correlation coefficient rapidly decreased from 0.8918 to 0.8801 at a depth of 20.0 mm.