## 4 Experiments and Results
### Infrared Image Super-Resolution Experiment with Added White Gaussian Noise  
In this experiment, the LR infrared images were generated by applying the two-fold down-sampling operator after which white Gaussian noise of different variance (\(\sigma=10,20,30,40\)) was added. In order to perform a fair comparison under noise, a denoising pre-processing step was added to the Bicubic. To evaluate the performance of the various methods objectively, PSNR and SSIM were calculated at the x2 super-resolving operator; these results are listed in Table 2.  
Figure 7: Super-resolution x4 results of the LR figure images without noise; (**a–d,i–l**) ground truth and the results of the Bicubic, MFT, TV, TGV, TV4, FTV4, and FTV4 Lp methods, respectively; (**e–h,m–p**) enlarged details from the rectangles in (**a–d,i–l**), respectively. \begin{table}
\begin{tabular}{r c c c c c c c c} \hline \hline \(\sigma\) & **Image** & **Birds** & **Streets** & **Crossroads** & **Building** & **Passerby** & **Figure** \\ \cline{2-9}  & **Method** & **PSNR/SSIM/TIME** & **PSNR/SSIM/TIME** & **PSNR/SSIM/TIME** & **PSNR/SSIM/TIME** & **PSNR/SSIM/TIME** & **PSNR/SSIM/TIME** & **PSNR/SSIM/TIME** \\ \hline Bicubic & 35.6726/0.8802/1.29 & 31.0675/0.8543/1.18 & 32.9044/0.8182/1.25 & 28.8987/0.8011/0.46 & 27.9384/0.8058/0.43 & 28.8686/0.8416/0.42 \\  & MFT & 34.803/0.8567/14.21 & 36.6493/0.8231/14.05 & 32.1554/0.7846/14.06 & **29.3813**/0.7704/3.39 & 28.6170/0.7620/3.41 & 29.6157/0.8134/3.47 \\  & TV & 35.8549/0.9101/7.39 & 30.2137/0.8295/0.91 & 32.3601/0.8010/7.94 & 28.5266/0.7889/3.81 & 28.5554/0.7808/3.69 & 28.4999/0.8066/4.57 \\
10 & TGV & 36.4840/0.9200/9.51 & **31.2637**/**0.8473**/9.12 & 32.8449/0.8329/9.91 & 32.6829/0.8045/3.68 & 28.7798/0.8090/3.97 & 28.7862/0.8522/4.84 \\  & TV & 36.1667/0.9112/7.91 & 30.5655/**0.8566**/**0.96** & 32.8811/0.8350/8.53 & 28.2922/0.7913/4.42 & **28.9438**/0.8088/3.37 & 28.8288/0.8625/4.61 \\  & FTV4 & 36.6335/0.9208/8.99 & 30.9376/0.8420/6.83 & 32.8552/0.8350/9.69 & 28.7223/0.8084/5.36 & 28.8201/0.8078/3.19 & 28.7438/0.8482/3.73 \\  & FTV4 Lp & **36.8411**/**0.9235**/9.19 & 31.7147/0.8460/7.62 & **31.2899**/**0.8371**/9.75 & 28.7996/**0.8096**/5.17 & 28.9227/**0.8109**/3.31 & 28.9178/0.8536/3.66 \\ \hline Bicubic & 32.1685/0.7628/1.84 & **28.9832**/0.7405/1.47 & 30.2125/0.7090/1.61 & 27.3900/0.6897/0.53 & 26.6925/0.6971/0.55 & 27.5348/0.7368/0.57 \\  & MFT & 29.3999/0.6507/14.04 & 27.8230/0.6641/14.06 & 28.8784/0.6540/14.22 & 27.0684/0.6513/3.32 & 26.0077/0.6193/3.34 & 22.2849/0.6460/3.32 \\  & TVAs is clear from Table 2, all the results of the TV-based method are poor. When \(\sigma=10\), the reconstruction results of MFT, TGV and TV4 in the streets, building, passerby and figure images are slightly superior to the proposed method; however, when \(\sigma\geq 20\), their reconstruction results are worse than the proposed method. Furthermore, although the FTV4-based method has no obvious advantage in the SRR with added white Gaussian noise at any particular level, its average result is still superior to the other three methods and is only slightly inferior to the proposed method. In addition, the computation time of all methods becomes significantly longer with an increasing amount of added white Gaussian noise, and the Bicubic method still takes the shortest amount of time among all methods. The proposed method takes almost the same amount of time as the FTV4 method, and longer than the TV4 method. Therefore, considering the PSNR, SSIM, and computation time, the proposed method performs significantly better than the other six methods in most cases. In Figure 8, three infrared images, which have added white Gaussian noise (\(\sigma=20\)) and were down-sampled by two-fold are shown as examples; the visual effects can still be observed in these images. From the reconstructed images in Figures 9-11, it can be observed that the images reconstructed using the Bicubic, MFT, and TV-based methods still contain considerable noise.