## 2 Materials and Methods
### Image De-Blurring  
Transillumination imaging techniques for visualizing absorbing structures within the body often encounter blurring. While both scattering and absorption contribute to image blurring, scattering plays a dominant role. Many research efforts have been made to overcome this challenge. In the previous studies of the group, the suppression of the scattering effects on the transillumination image was carried out by deconvolution with the depth-dependent PSF, and the deep learning scatter blurring method has also proved to be feasible and efficient [5; 6; 7; 10; 12]. However, these methods still have some limitations in implementation, such as the imperfection of the deconvolution technique, the long computation time, the computational hardware requirements, and the limitation of effective de-blurring shallower than 15.0 mm. In the previous study, we employed fully convolutional networks (FCN) based on the U-net with skip connections. The training process for the scattering de-blurring model is visually represented in Figure 3, offering a clear visualization of the methodology employed. The results show that we can obtain a clear image of the absorbing structure as deep as several to 10.0 mm in a turbid medium. To address this challenge, the Attention U-Net model and the Attention Res-UNet model were incorporated for the de-blurring process [16; 17]. The attention gate is a mechanism that selectively emphasizes specific regions of interest while suppressing the activation of irrelevant regions on a given input feature map \(X\). To achieve this, the attention gate takes advantage of a gating signal \(G\in\mathbb{R}^{C^{\prime}\times H\times W}\), which is obtained at a coarser scale and incorporates contextual information. When additive attention is employed, the attention gate calculates the gating coefficient. Initially, both the input \(X\) and the gating signal \(G\) undergo linear mapping to a \(\mathbb{R}^{F\times H\times W}\) dimensional space. Subsequently, the output is compressed in the channel domain to generate a spatial attention weight map \(S\in\mathbb{R}^{1\times H\times W}\), as shown in Figure 4. The entire process can be formulated as described in Equation (3) \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Training** & **Validation** & **Testing** & **Total** \\ \hline De-blurred & 5600 & 1600 & 800 & 8000 \\ Estimate depth & 56,320 & 14,080 & 7040 & 70,400 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dataset for training, validation, and testing of scattering de-blurring and depth estimation. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **De-Blurred** & **Depth Estimation** \\ \hline \(\mu_{s}^{\prime}\) & 1.0 mm\({}^{-1}\) & 1.0 mm\({}^{-1}\) \\ \(\mu_{a}\) & 0.00536 mm\({}^{-1}\) & 0.00536 mm\({}^{-1}\) \\ \(d_{\text{min}}\)-\(d_{\text{max}}\) & 0.1–20.0 mm & 0.5–20.0 mm \\ Step depth & 0.1 mm & 0.5 mm \\ Batch size & 8 & 32 \\ Learning rate & \(10^{-4}\) & \(10^{-4}\) \\ Epoch & 100 & 20 \\ Loss function & Dice-coef loss & Categorical Cross-entropy \\ Optimizer & Adam & Adam \\ Input shape & \(256\times 256\times 1\) & \(224\times 224\times 1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters for de-blurred and depth estimation models. and Equation (4) [18], where \(\phi\), \(\phi_{x}\), and \(\phi_{g}\) are linear transformations implemented as convolution \(1\times 1\). \[S=\sigma\big{(}\varphi\big{(}\delta\big{(}\phi_{x}(X)+\phi_{g}(G)\big{)}\big{)} \big{)} \tag{3}\]  
\[Y=SX \tag{4}\]  
Residual blocks, which are skip-connection blocks, are designed to learn residual functions by referring to the layer input instead of learning unreferenced functions. These blocks were originally introduced as a component of the Res-Net architecture. In a formal sense, denoting the desired underlying mapping as \(H(x)\), the stacked non-linear layers aim to approximate an additional mapping that captures the difference between the current  
Figure 4: The diagram of the attention gate.