## 4 Experiments
### Examples of Integrity Authentication  
Before fully comparing our proposed algorithm and existing algorithms, we first conducted a preliminary comparison of the algorithms through a set of integrity authentication instances, as shown in Figure 5. Figure 5a shows the original HRRS image stored in TIFF format, while Figure 5b-h can be divided into 2 groups: instances that do not change the content of the image, and instances that change the content of the image.  
Figure 5: Integrity Authentication Examples for HRRS image: (**a**) original HRRS image; (**b**) formatted image (TIFF format to BMP format); (**c**) the image after watermark embedding (least significant bit algorithm as an example, embedding 128-bit watermark information); (**d**) JPEG-compressed image; (**e**) subject-unrelated tampering; (**f**) subject-related tampering; (**g**) \(8\times 8\) random tampering; (**h**) \(16\times 16\) random tampering.  
In the first group, Figure 5b-d, the operation of the images was: format conversion (TIFF format to BMP format), digital watermark embedding (using the least significant bit algorithm), and 95% JPEG compression. In the first group, each HRRS image carried the same content as the original image shown in Figure 5a. The human eye could not even distinguish whether these images were different from original; however, they were changed drastically at the binary level.  
The second group, Figure 5e-h, contains an image with subject-unrelated tampering, an image with subject-related tampering, an image with an area of 8 \(\times\) 8 pixels randomly tampered with, and an image with an area of 16 \(\times\) 16 pixels randomly tampered with, respectively. Obviously, the contents of the second group of HRRS images were tampered with. Their binaries were also changed dramatically.  
Normalized hamming distances between hash sequences of Figure 5a and each image of Figure 5b-h are shown in Table 2. Table 3 shows the integrity authentication results, based on Table 2, when the threshold \(T\) was 0.02.  
Comparing the performance of each algorithm, shown in Table 3, we observed that only our algorithm and the AAU-Net-based algorithm simultaneously kept robustness to the operations, shown in Figure 5b-d, and tampering sensitivity to the malicious tampering, shown in Figure 5e-h. Even compared with AAU-Net-based algorithms, our algorithm performed better for the operations shown in Figure 5b-d, and more sensitively to tampering for the operations shown in Figure 5e-h. Although the Attention ResU-Net-based  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\
\begin{tabular}{c} **Model Each** \\ **Algorithm Was** \\ **Based on** \\ \end{tabular} } & **Figure 5b** & **Figure 5c** & **Figure 5d** & **Figure 5e** & **Figure 5f** & **Figure 5g** & **Figure 5h** \\ \hline \multirow{2}{*}{
\begin{tabular}{c} MUM-Net \\ MultiResUnet \\ U-net \\ M-net \\ M-net  
algorithm and the Swin-Unet-based algorithm also had good robustness, they performed poorly in tampering sensitivity, failing to fully detect the tampering shown in Figure 5e-h.  
In the actual integrity authentication, different thresholds are often set for different scenarios or authentication needs. Tables 4 and 5 show the results of integrity authentication, based on Table 2, with \(T\) set to 0.05 and 0.01, respectively.  
As demonstrated in Table 4, the MultiResUnet- and Attention R2U-Net-based algorithms also kept robustness to Figure 5b-d and detected the tampering shown in Figure 5e-h when threshold \(T\) was 0.05. However, one can also from Table 5 that only our algorithm maintained both robustness and tampering sensitivity when \(T\) was reduced to 0.01.  
Tables 2-5, our algorithm and AAU-Net-based algorithm performed better than others. Our algorithm was also more robust than AAU-Net-based algorithms. Overall, our improved Swin-Unet-based algorithm achieved the best integrity authentication results, as shown in Figure 5.