# Deep Residual Network with Sparse Feedback for Image Restoration
## 4 Experiments and Analysis
### Human Face Database  
To train FbResNet for motion deblurring with unknown motion direction, we consider four different motion directions: up, down, left, and right. The database used in this paper includes 1403 human faces. These faces are divided into two parts: 1044 images are used to train the parameters of FbResNet, and the remaining 359 images are used to test the network. The size of the human face image is 64 \(\times\) 64. In this database, the technology of patch cutting is not adopted because the size of the input image is already small.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Structure** & **ResNet** &
\begin{tabular}{c} **ResNet with Dilated** \\ **Convolution** \\ \end{tabular} & **DnCNN** & **FbResNet** \\ \hline Input image & blur image & blur image & blur image & blur image \\ Number of layers & 10 & 10 & 10 & 10 \\ Padding strategy & Same & same & symmetric & same \\ Dilation convolution & No & yes & yes & yes \\ Output image & clear image & clear image & residual image & clear image \\ \hline \hline \end{tabular}
\end{table}
Table 1: Experiment setting of different models.  
Figure 2: The architectures of the reformed ResNet and denoising convolutional neural network (DnCNN). (**a**) ResNet; (**b**) ResNet with dilated convolution; and (**c**) DnCNN.  
Figure 3 shows the restored images of human face. The first row shows the images with motion blur; the second row shows the deblurred images of DnCNN; the third row shows the deblurred images of ResNet with dilated convolution; the fifth row shows the deblurred images of FbResNet; and the last row shows the clean images. The restored results of FbResNet are clearer and more similar with the ground truth (clean images) than those of the other models.  
In addition, we find that the restored images using DnCNN and FbResNet are darker than the other ones (the fifth column of Figure 3). The main reason is that there are a few feedbacks or no feedback in these two network structures. Hence, the network structure with a few feedbacks can maintain the average skin color of the restored face image and avoid overexposure, even if the input image has a small exposure effect.  
Figure 4 shows the enlarged image of a human face. From left to right, it is the restored image of DnCNN, ResNet, ResNet with dilated convolution, FbResNet, and the ground truth, respectively. It is easier to see the advantages of FbResNet, which has less deformation and higher resolution than those of other models. Figure 5 shows the restored images with motion blur in different directions. The first row shows the blur images and the second row shows the deblured images; the below words describe the movement direction of the produced blur images. We find that the robust performance of FbResNet for motion blur is generally good, but the more mixture of the movement direction, the performance will gradually decline, and the deblurred robustness for various directions needs to be further improved.  
Figure 4: Enlarged restored images. From left to right, it is the restored images of DnCNN, ResNet, ResNet with dilated convolution and FbResNet, and the last is the clean image.  
Figure 3: Restored images of human face. The first row shows the images with motion blur; the images from the second row to the fifth row are restored images of DnCNN, ResNet, ResNet with dilated convolution and FbResNet; the last row shows the clean images.  
The left figure in Figure 6 shows the average peak signal-to-noise ratio (PSNR) improvement over the other models with respect to different motion direction by PbResNet model. It can be seen that the proposed FbResNet consistently outperforms the other models by a large margin. The right figure in Figure 6 shows the convergence of the loss function. The convergence speed of FbResNet model is faster than that of the other network models.