## 2 Materials and Methods
### Pixel-by-Pixel Scan Matrix Method  
Reconstructing 3D structures from the combined information from the FCN (Attention Res-UNet) and CNN (DenseNet-169) model represents a significant advance in image processing and analysis. This approach leverages the power of deep learning to effectively address the challenges posed by scattering in transillumination images of absorbing structures in a turbid medium. As mentioned above, when processing an acquired image for complex structures that are present in a scattering medium or a network structure such as blood vessels, current solutions apply a subdivision of the observed image by dividing it into many separate parts [27; 29]. Each section will contain an image of a separate light-absorbing structure. This leads to limitations in processing complex images such as blood vessels when many structures are present in the same image area. In Figure 3, the operational principle of the pixel-by-pixel scan matrix method is elucidated. The gray zone matrix depicted, which encompasses pixels \(B\times B\), represents the blurred image under consideration. Currently, the green zone matrix, which extends over \(S\times S\) pixels, serves as the scanning matrix. The application of a zero-padding technique generates an augmented image of dimensions \((2S+B-2)\times(2S+B-2)\) pixels, thus providing additional data points for analysis. Throughout the computational process, the scanning matrix navigates laterally from left to right and subsequently from the upper to lower regions of the zero-padded image. Each pixel, or computational cell, within the scanning matrix, is evaluated using a FCN/CNN model. Subsequently, the estimated value is logged into a string corresponding to that specific pixel. Upon completion of the scanning process, the value that manifests the highest estimated frequency is selected as the definitive value for the related pixel, as mathematically articulated in Equation (3). Therefore, this method provides a comprehensive pixel-wise analytical approach that potentially improves the clarity and accuracy of biomedical imaging, particularly in applications that require meticulous resolution and exact detail. \[\text{Mode}=\{x_{i}\,|\,\text{frequency}(x_{i})=\text{max}\,\text{frequency}\} \tag{3}\]  
Figure 4 shows examples of the estimated pixel value in the case of the de-blurred mode and the depth estimation, respectively. The de-blurring process for a \(3\times 3\) blurred image, depicted in yellow and processed with a \(2\times 2\) green kernel matrix as the output of a de-blurring model, involves four distinct sliding steps, labeled step I, II, III, and IV, as demonstrated in Figure 4A. Upon examining the pixel at coordinates \((2,2)\), the de-blurring sequence reveals values of 0, 1, 1, and 1 for each respective step. This effect results from the binary of the image's training mask data, which confines pixel intensity values to either 0 or 1. Consequently, the de-blurring model's output is binary, limited to these two values. According to Equation (3), which returns the result with the highest frequency in the set, the value of the pixel at coordinates \((2,2)\) is computed to be 1. Then, this procedure is systematically replicated for the remaining pixels in the \(3\times 3\) matrix. The Fully Convolutional Network (FCN), specifically an Attention Res-UNet, plays a pivotal  
role in the de-blurring and restoration of the de-blurred image. With a matrix size of \(256\times 256\) pixels, the FCN model analyzes the blurred image pixel by pixel, employing a one-pixel step size. This approach minimizes the effects of scattering, resulting in a clear and sharp 2D image that enhances the visibility of absorbing structures. However, the sliding process may occasionally lead to pixel deficits at the image's edges. To address this issue and ensure uniform processing of all image regions by the FCN model, we employ the zero-padding technique.