## 5 Conclusions  
The de-blurring and estimation depths of the absorbing structure in transillumination images taken through a turbid medium such as biological tissue have attracted significant interest among researchers and experts in biomedical optics in recent years. This study addresses the challenge of de-blurring and depth estimation in transillumination images by utilizing the dependent point spread function (PSF) derived for the light source within a scattering medium. The neural network (NN) technique is employed to find the deep learning models capable of de-blurring the image and estimating the depth of the absorption structure inside a turbid medium. The effectiveness of deep learning for de-blurring transillumination images and also depth estimation has been successfully demonstrated for depths ranging from 0.1 to 10.0 mm in previous studies. Although previous attempts have been made to enhance blurred images, the technique proposed in this study offers another solution. The attention gate and the residual block were proposed to de-blur the image. Attention Unet and Residual Unet models were examined compared to the Unet model. Attention Unet and Residual Unet models yielded better performance than the Unet model. Attention Res-Unet then examined the performance compared to Attention Unet. Both the Attention U-Net and Attention Res-UNet models achieved correlation coefficients exceeding 88% even at a depth of 20.0 mm, affirming the applicability of deep learning models to de-blur transillumination images. Finally, Attention Res-Unet shows better performance in terms of the correlation between a de-blurred image and the original given image. The impact of image size on the result was also investigated. To ensure a better result with a deep-absorbing structure, the image size in a dimension should be more significant than three times the standard deviation of the light distribution on the medium's surface when calculating the turbid medium's deepest light point source distribution. This study examined four different models, ResNet-50, VGG-16, VGG-19, and DenseNet-169, to estimate the depth of the absorbing structure. DenseNet-169 demonstrates superior performance among these models, achieving an accuracy rate greater than 65%. This research and the generated dataset prove valuable in accurately estimating the depth of the absorption structure from transillumination images. The evaluation of 1600 test images at 40 different depths ranging from 0.5 mm to 20.0 mm yielded a correlation coefficient of \(R^{2}=0.9911\), which affirms the feasibility of the DenseNet169 model in estimating the depth of the absorbing structure. It should be noted that this proposed technique requires a substantial amount of training data and computational power. However, these challenges can be addressed through the appropriate selection of PSFs and advances in computing capabilities. Consequently, this study confirms the feasibility of deep learning in clarifying blurred images and estimating the depth of absorption structures using PSF and CNN models based on training data. Figure 17: Correlation analysis of given and estimated depths. The de-blurring and depth estimation results obtained for absorption structures at depths from 0.1 to 20.0 mm are highly satisfactory. These findings indicate the usefulness of the proposed methods for observing subcutaneous structures, identifying tumors and small animal parts, and determining depth distributions up to 20.0 mm. In particular, this technique is based solely on computer vision without complex exposure, ultrasound, or additional substances. Therefore, it presents a novel tool for the diagnosis of dermatological diseases, various tumor-associated diseases, vascular diseases, and tissue metabolism. The results of this study contribute to the development of depth estimation and de-blurring methods using deep learning models. Furthermore, merging two targets identified by a single deep learning model will enable the definition of multiple depths within a single image.