## 4 Experiments
### Comparison with the State-of-the-Arts  
To demonstrate the effectiveness of our proposed method, we conduct a comparison with several state-of-the-art methods. These include two GAN-based methods (SRResNet [29] and RCAN [38]), three attention-based methods (SPARNet [10], SISN [11], and IGAN [39]), and two transformer-based methods (SwinIR [17] and Uformer [15]). We evaluate these methods on the CelebA and Helen datasets, along with the real face images. In addition, we apply bicubic interpolation as the baseline for comparison. All models are trained on the same CelebA dataset to ensure a fair comparison. The quantitative results are tabulated in Table 6.  
(2) _Comparison on Helen dataset_: Aiming to prove the flexibility of the proposed model, we assess its performance on the Helen dataset using the same model trained on CelebA. We present a quantitative and visual comparison of the proposed method with others on the Helen dataset in Table 6 and Figure 7, respectively. According to the results, the proposed method still shows superiority in restoring facial images both quantitatively and qualitatively. This proves the robustness and stability of the proposed method. However, it is worth noting that all methods experience a decrease in performance when the training and testing images are not from the same dataset. Therefore, investigating the styles among various datasets will be a promising way to enhance the generality of FSR methods in the future. (3) _Comparison on real face images_: Restoring face images from real-world environments is a challenging task due to the complexity of the captured images. Although the CelebA dataset is a good source for simulating face images, it cannot replicate all the complexities of real-life scenarios. In order to test the effectiveness of the proposed method in restoring real-world face images, we conduct experiments on low-quality face images collected from the classic TV series \"Friends\". It was shot in the 90s with low-tech imaging equipment and suffered severe low-resolution issues, making it perfect for testing. The experiment results are illustrated in Figure 8. Benefiting from the guiding blocks pointing to the key features and the pixel-related upsample layer preserving face structures, our method reconstructs more detailed facial images with appealing facial structures compared with other state-of-the-art methods. Figure 8: Visual comparisons for x8 SR on real face images. Please zoom in for better comparison. Figure 7: Visual comparisons for x8 SR on the Helen test set. Please zoom in for better comparison. Experiments in this subsection are conducted on the same 1000 test face images from the CelebA dataset as above. The noise images are multiplied by 0.3 and then added to the original HR images to simulate the noise-degrading process, except for the salt-pepper noise that directly operated on the original HR images. All the noise generation models can be obtained from Numpy [62]. To make a fair comparison, we manually alternate the parameters of these noise models by adjusting the PSNR of their HR outputs to 26.0-26.5 dB. Here are the detailed parameters of the noise models: The Gaussian noise has a mean value of 0 and a standard deviation of 70. The Poisson noise has a lambda value of 50, while the Rayleigh noise has a scale of 40. The gamma noise has a shape of 7 and a scale of 7. The exponential noise has a scale value of 43. The uniform noise has a low value of 20 and a high value of 80. Lastly, the probability of the salt-pepper noise is set to 0.01. The noise images and their HR outputs are shown in Figure 9.  
These HR images, which have been impaired by noise, are /8 downscaled and subsequently directed through the proposed method. Additionally, we introduce the bicubic interpolation results as the baseline while choosing the best comparative method, Uformer, for better comparison. Table 7 and Figure 10 show the quality evaluation matrices and visual comparisons, respectively.