# CTprintNet: An Accurate and Stable Deep Unfolding Approach for Few-View CT Reconstruction
## 5 Results and Discussion
### Results on a Synthetic Dataset  
We first tested the algorithms on the synthetic dataset \"Contracted Overlapping Uniform Lines and Ellipses\" (COULE) ([[https://www.kaggle.com/datasets/loiboresearchgroup/coule-dataset](https://www.kaggle.com/datasets/loiboresearchgroup/coule-dataset)]([https://www.kaggle.com/datasets/loiboresearchgroup/coule-dataset](https://www.kaggle.com/datasets/loiboresearchgroup/coule-dataset)), accessed on 13 November 2021), which contains 430 sparse-gradient grayscale images of size \(256\times 256\). Among the 430 images, we used 400 for training and the remaining 30 for the test phase.  
Experiment A. In this experiment, we trained and tested CTprintNet and LPP considering data without noise. From Figure 5, showing the boxplots relative to PSNR, SSIM (in blue for LPP and in orange for CTprintNet), we can see that LPP defines better reconstructions, on average. In fact, it is well known that the post-processing architectures perform particularly well in standard conditions where the training and testing data are obtained from similar conditions.  
Experiment B. Under real conditions, however, the projection data are naturally compromised by noise. To test the stability of the proposed framework with respect to noise in the sinogram, we first analyzed the behavior of the architecture when varying the values of the noise's standard deviation \(\sigma\) introduced in the training and test phases. In Experiment B, we trained the two architectures by adding Gaussian noise as in (30) with \(\sigma=0.05\) both to the training set and test set. The results obtained, shown in Figure 6, demonstrate that noise influences the performance of the two architectures, which now are more competitive with each other. In particular, the SSIM index, indicating the visual quality of the image, is far better for CTprintNet.  
Experiment C. Since it is well known that a drawback of neural networks, particularly post-processing ones, is that their performance on data never seen or far from the training data is not always satisfying, in Experiment C, we trained the two architectures without noise on the data (\(\sigma=0\)), and we tested them with variable standard deviations in the interval \([0,0.06]\). In Figure 7, we plot the average values of the two metrics as the standard deviation of the noise added on the test set changes (the blue and red lines correspond to LPP and CTprintNet, respectively). The results clearly show that the proposed architecture is stable with respect to noise, whereas the LPP initially provides better performance; however, as the noise increases, its behavior worsens considerably (see also the reconstructions of a representative test image in Figure 8). Conversely, CTprintNet is able to guarantee good results by limiting the damage caused by increased noise despite being trained with noise-free images.  
Figure 5: Boxplots of the PSNR (**left**) and SSIM (**right**) concerning LPP (blu line) and CTprintNet (orange line) for the COULE dataset without noise in the training and in the testing images. The red line indicates the median, and the black line indicates the mean value.  
Figure 8: Experiment C: from left to right, the ground truth of one test image and the reconstructions obtained with CTprintNet (**top row**) and LPP (**bottom row**) with increasing noise levels on the sinogram.  
Figure 6: Boxplots of the PSNR (**left**) and SSIM (**right**) concerning LPP (blue line) and CTprintNet (orange line) for the COULE dataset with noise given by \(\sigma=0.05\) in the training and in the testing. The red line indicates the median, and the black line indicates the mean value.  
Figure 7: Trends of average values of PSNR (**left**) and SSIM (**right**) as functions of the standard deviation of the noise added to the test set, in blue for LPP and in red for CTprintNet, considering the COULE dataset and trained without noise. Bars and shades indicate standard deviation values over the test set images.