# Internet Video Delivery Improved by Super-Resolution with GAN
## 7 Experimental Results
### Perceptual Quality and JND  
This subsection analyzes how the perceptual and pixel-wise metrics perceive video compression distortions. First, we examine the JND mapping, using the QP to obtain the desired video bitrates. Then, for the same set of video bitrates, we examine the PSNR mapping. [PERSON] et al. [48] presented JND mapping of the analyzed video sequences.  
Figure 5a shows the outcomes for a 1080p video sequence, #112 of the VideoSet dataset. This video sequence was encoded using a broad range of bitrates from 94 kbps (\(QP=47\)) to \(264,088\) kbps (\(QP=7\)). From a pixel-wise point of view, the general conclusion was that the encoding bitrate increases quickly as the quantization parameter decreases. A small QP indicates that the encoding process uses a low compression rate. Moreover, PSNR mapping can capture the changes in the encoding bitrate as it transitions from low to high values.  
From a perceptual point of view, the JND mapping identified three distortion points, i.e., \(QP=\{21,27,31\}\), perceived by the human vision system. In other words, QP values taken from the encoding spectrum \([0,21[\) will result in encoding distortions unnoticed by the human visual system. Similar conclusions were derived for other encoding spectra: \(QP=\{[21,27[\), \([27,31[\), \([31,51]\)}. These values are closely related to the analyzed video  
Figure 4: Perceptual quality assessment of videos \(2\times\) upscaled by SR methods given videos with different bitrates. (**a**) VMAF scores for videos encoded at different bitrates. (**b**) VMAF scores for videos encoded with different quantization parameters.  
Figure 5: Visual perception analysis of \(V^{SR}\) super-resolved videos. (**a**) Comparing JND and PSNR sensitivity to video distortion. (**b**) Comparing \(V^{SR}\) encoded with \(QP=0,15,20\) and the JND points 1 st, 2 nd, and 3 rd.  
sequence. Still, the general conclusion is that human vision cannot perceive visual quality improvements among encoded videos in the same encoding spectrum.  
The super-resolved video sequences (\(V^{SR}\)) were analyzed to determine their closest ground-truth encoded versions (\(V^{HD}\)) and map the reconstructed video sequence to the \(\mathrm{JND}\) encoding spectrum associated with the ground-truth video sequence. Equation (10) calculates the distance between the reconstructed video sequence and all encoded video sequences.  
\[QP_{V^{SR}_{i,k}}=j,\text{where }j=\min\left(D\left(V^{SR}_{i,k},V^{HR}_{i,j} \right)\right) \tag{10}\]  
\(D\) is the perceptual distance LPIPS; \(k=\{0,15,20\}\) is the \(QP\) used to encode the video sequence that was in the restoration, among \(i=\{1,\ldots,220\}\) possibilities; \(j=\{7,\ldots,47\}\) is the \(QP\) of encoded video sequences \(V^{HR}\); \(V^{SR}_{i,k}\) is given by  
\[V^{SR}_{i,k}\in\left\{\begin{array}{ll}&Q_{1},\text{ if }QP_{V^{SR}_{i,k}}<QP_{1^{ \ast}l,l,j}\\ &Q_{2},\text{ if }QP_{1^{\ast}l,jND,i}\leq QP_{V^{SR}_{i,k}}<QP_{2^{\ast}l,ND,i}\\ &Q_{3},\text{ if }QP_{2^{\ast}l,ND,i}\leq QP_{V^{SR}_{i,k}}<QP_{3^{\ast}l,ND,i}\\ &Q_{4},\text{ if }QP_{V^{SR}_{i,k}}\geq QP_{3^{\ast}l,ND,i},\end{array}\right.\]  
where \(QP_{1^{\ast}l,IND,i}\), \(QP_{2^{\ast}l,IND,i}\), and \(QP_{3^{\ast}l,IND,i}\in\)\(QP_{V^{HR}_{i,k}}\).  
Figure 5b shows all 1080p video sequences from the VideoSet dataset, with JND points calculated using Equation (10). We calculated these points for video sequences encoded using \(QP=\{0,15,20\}\) and those super-resolved by the VSRGAN+ model. When the ground-truth video sequences were encoded using \(QP=\{0,15\}\), the evaluation showed that 100% of the super-resolved video sequences were within the set \(Q_{1}\). The ground-truth video sequences, encoded with \(QP=20\), included 91.4% of the super-resolved video sequences in \(Q_{1}\) and 8.6% in \(Q_{2}\). In summary, the super-resolved video sequences had a perceptual quality similar to their ground-truth counterparts.