## 4 Results and Discussion
### Application of Estimated Parameters to Reconstruction of Larger Images  
Considering larger images and sinograms in practical CT applications, the significant increase in network size and training cost leads to problems of increased computer memory and computation time. To avoid these problems, we propose the following solution. First, a small reconstructed image and the corresponding projection are prepared as training data. These small-sized data are used to construct the optimizer \(\Lambda\) in a training manner. When estimating parameters from the original projection numbers, the projection is reduced to the same size as the training data and input to the optimizer. Then, the estimated parameters are used to reconstruct the image from the original projection. In this subsection, we verify the feasibility of this procedure by showing that the estimated parameters can be used to reconstruct a larger projection than that used for training.  
We generated projections \(y^{6},y^{7},\ldots,y^{10}\), which were magnified versions of projections \(y^{1},y^{2},\ldots,y^{5}\). These projections were generated from phantoms \(e^{6},e^{7},\ldots,e^{10}\) shown in Figure 12, which were enlargements of \(e^{1},e^{2},\ldots,e^{5}\). The projection noise level to be applied was the same as in the previous subsection. The number of projection directions was increased to \(180\) so that the inverse problem would not be unduly difficult due to the large image size \(128\times 128\). In the proposed use case, the parameters are estimated on the basis of  
Figure 11: Contour map of evaluation function values \(D(\ell,z(K))\) with projection \(y^{\ell}\) for parameters \(\gamma,\alpha\). Blue and red points indicate \(\hat{\lambda}^{\ell}\) and \((1,1)\) corresponding to the MLEM algorithm, respectively.  
a smaller projection reduced from the larger projection, but here the procedure is inverted. That is, the image reconstruction of projection \(y^{\ell}\) for any \(\ell=6,7,\ldots,10\) uses the parameter \(\lambda^{\ell-5}\) estimated from its smaller version, projection \(y^{\ell-5}\).  
Figure 13 plots the values of the evaluation function during reconstruction. The same trend as in Figure 10 is obtained when the parameters estimated from the reduced projection are diverted. The contour maps of the parameters shown in Figure 14 are also consistent with the trend in Figure 11, suggesting that it is possible to use the parameters estimated from the miniaturized projection. Although developing a method to reduce the size of the large original projection appropriately is required for actual use, the results show the possibility of a practical application.  
The reconstructed and subtraction images from the true value on the test data \(\ell=6\) and \(\ell=8\) are shown in Figures 15 and 16. The images reconstructed by the MLEM algorithm and their subtraction images are also shown for comparison. Comparing the reconstructed images for \(\ell=6\), it can be seen that the images of  
Figure 14: _Cont._  
Figure 14: Contour map of evaluation function values \(D(\ell,z(K))\) with projection \(y^{\ell}\) for parameters \(\gamma,\alpha\). Blue and red points indicate \(\hat{\lambda}^{\ell-5}\) and \((1,1)\) corresponding to the MLEM algorithm, respectively.