## 5 Discussion  
The authentication of HRRS image is essentially concerned with the integrity of the effective content of the image, rather than the changes in the data carrier itself. Therefore, the traditional authentication methods, such as cryptography-based methods and digital-watermark-based methods, do not adequately address the problem of authentication for HRRS images. Although perceptual hash algorithms can achieve perceptual-content-based authentication for conventional image data, the existing research results still have large deficiencies for the authentication of HRRS images, especially in terms of tamper sensitivity and robustness.  
Tamper sensitivity and robustness are the two most important attributes of perceptual hashing, but the two are often contradictory. The key to solving this contradiction lies in how to extract the robust features of the image. Based on deep learning theory, we introduce the classic network model U-net to improve the robustness of perceptual hash algorithm while maintaining the tamper sensitivity. Another important contribution of our algorithm is that we propose a training sample generation method combining Canny operator and artificial processing to meet the high accuracy requirement of training samples for authentication.  
Through the above experiments in Sections 4.2-4.4, it can be seen that compared with conventional perceptual hash algorithms and the algorithm in [10], the advantage of our algorithm is that the algorithm has better robustness and maintains favorable tamper sensitivity. Moreover, the training of the modified U-net model requires only 50 pairs of training samples, which basically meets the expectation.  
Of course, although the algorithm has better tamper detection capability than most image perceptual hash algorithms, it cannot accurately detect all of the malicious tamperings. In the experiments in Section 4.4, a few malicious tampering instances escaped the detection of our algorithm. In fact, the tamper detection capability of our algorithm can be adjusted by changing the algorithm parameters or threshold. For example, we can set the threshold \(T\) lower to improve the sensitivity of the algorithm to detect more subtle malicious tampering, which will have a certain negative impact on the robustness of the algorithm, or, in the phase of PCA-based feature compression, we can extract more principal components of the feature matrix to generate longer perceptual hash values, but it may affect the compactness of the algorithm. In summary, if the algorithm is over-emphasizing the ability to detect subtle tamperings, other aspects of the algorithm would be affected.  
At present, although our work obtained a relatively good result, it is still possible to be improved in future work. (1) HRRS images tend to be relatively large in size, and often cannot be authenticated as a whole like conventional images but are segmented into small images for authentication. Thus, how to ensure the continuity of information between sub-images is a question that needs further study. (2) Tampering positioning allows the perceptual hash algorithm to not only authenticate the content integrity of the HRRS image, but also determine where the HRRS image has been tampered with. However, the tampering positioning accuracy of the existing perceptual hash algorithms is not ideal. Therefore, higher precision tampering positioning method still needs further research.