# Deep Learning of Diffuse Optical Tomography Based on Time-Domain Radiative Transfer Equation
## 5 Discussion
### Comparison with the Conventional DOT Method  
Here, we compare the results by our deep learning method with the profile reconstructed by the conventional DOT method [17]. The differences emerge in two ways, that is, in solving the forward problem and the inverse problem, respectively. On the forward problem, the conventional DOT method [17] solves a diffusion equation to trace light propagation. On the other hand, we use RTE calculation that gives us more accurate data. On the inverse problem, one can reconstruct the image by estimating the mean, variance, and skew of DTOF in the conventional DOT method. However, it makes the reconstructed image unclear due to hyperparameter problems. Therefore, here, we use the deep learning method to solve the inverse problem. The comparison between our deep learning method and the conventional DOT method is shown in Figure 12. The absorption coefficient and position reconstructed by the conventional method is shown by a pink line. This method gives a broader profile, compared to the true value. The absorption coefficients presumed by the deep learning are shown by a blue line. The blue lines show the primary candidate by the deep learning, where the absorption coefficient and position are well presumed compared to the true values. In the present deep learning, it is possible to presume the absorption coefficient and position more accurately. We also compared a higher resolution model using 168 domains. In the right panel of Figure 12, the location of the absorber is identified by a sharp boundary without spatial spread, which comes from a hyperparameter in the conventional DOT method. Thus, our deep learning scheme can provide a more reliable reconstruction method compared to the conventional DOT method. In addition, see [13], which shows a possibility of giving a good reconstructed image since a similar situation can be improved. We tested the RNN approach to classify the position. The model with RNN shows 20 percent lower accuracy for classification of 28 domains with the same setting. The LSTM approach has an advantage of analyzing data in chronological order. We also tested this RNN approach to predict for the same experimental data above used. The result tells us the wrong prediction that is caused by identifying some data in the wrong position. It is useless to reconstruct the image. The reason why the RNN gives a bad prediction is not good for analyzing long time sequence data, which has long term changes over time. It means that the RNN approach is not suitable for such time sequence. In Ref. [14], they showed the overview of DOT by using deep learning, and there is a good possibility to solve the inverse problem by using deep learning. They tested that propagation of light through the digital phantom and reconstructed image by using deep learning to solve the inverse problem. The result shows a remaining background noise on the reconstructed image. This is related to the fact that their algorithm has hyperparameters for both solving the inverse problem and reconstructing the image. On the other hand, to solve the inverse problem, we try to identify the position by using LSTM deep learning. Its process does  
Figure 12: Comparison of the present method with the conventional DOT method. The true absorption coefficient is shown by the dotted line. The pink curve depicts the reconstructed coefficient using the conventional DOT method. The blue line represents the probability distributions of the absorption coefficients predicted by our deep learning method, where the setup is the same as Figure 1. The **left (right)** panel is used by resolution as 28 domains (168 domains). not basically contain a hyperparameter and such parameters can be fixed through every learning step, and it is possible to make the reconstructed image clear when one takes more high resolution. They also showed that the deep learning approach to solve the inverse problem is highly dependent on the type of datasets used. We used the time dependent data to reconstruct the absorber's position.