## 4 Proposed Scheme for Self-Embedding
### Watermark Extraction and Reconstructing Ambtc
The Tampering Rate (TR) for the marked cover-image (Lena) ranged from 5% to 45%. Both methods proposed by [PERSON] & [PERSON] [30] and [PERSON] et al. [25] measured about 35 dB when the TR was 5%, and there was a slight difference in the performance of the two methods until the TR reached about 20%. However, the PSNR of the two showed similar reduction, and when TR was 20%, it was about 30 dB. Then, the PSNR of [PERSON] et al. [25] decreased to a smooth descending curve and was about 24 dB when TR = 45%, while the method proposed by [PERSON] & [PERSON] [30] drastically decreased to about 11 dB when TR = 45%. One of the reasons [PERSON]'s method [30] did not perform well is because it uses simple binary operations to detect the tampering area. This seems to be due to the threshold error according to the use of binary operations. [PERSON] et al. [25] used the 7 MSB binary value of each block for image authentication. Although [PERSON] et al. 's authentication method performed better than [PERSON] [30], authentication failures may occur due to errors caused using binary numbers and may affect performance. Figure 6: Tampered images at various tampering rates (%). Using halftones for image restoration is important to investigate. The image quality obtained by restoration using halftones was around 30 dB, which is a bit insufficient to ensure high image quality. The reason is that in the process of converting halftone to a grayscale image, it is visually observed that the quality of the image is clearly different from the texture of the original image. This means that the halftone could not be enough for the recovery bits. The PSNR of [PERSON] & [PERSON] [27] was limited from about 35 dB (highest) to about 24 dB (lowest), but it showed a relatively stable PSNR performance. For tampering authentication, they used [PERSON]'s watermarking technique [28], and its plan had a good impact on performance. When the TR was 5%, the PSNR of [PERSON] et al. 's method [17] and the proposed method were shown at about 39 dB and about 40 dB, respectively. The proposed method decreased slowly until TR = 45%, and when TR = 45%, PSNR was 36 dB. On the other hand, the PSNR of [PERSON] et al. [17] was about 25 dB (TR = 45%), which appeared as a slightly steeper curve than ours. However, the advantage of this method is that it is designed to prevent tampering coincidence problems, which has a positive effect on performance and shows superior performance among existing methods. Nevertheless, the proposed method shows good performance among self-embedding methods. The factors for improving the performance of the proposed method are as follows: first, the recovery bits for a specific block were stored in a long block located as far away as possible. Second, there was correct detection of tampered blocks. Since our proposed method was faithful in this perspective, we find that it had a positive effect on performance. Table 3 shows a comparison of the PSNR of the marked image and the restored image obtained after applying various self-embedding watermarking methods to the Lena image. Looking at the PSNR of the reconstructed image in Table 3, we show that the proposed method was superior to the previous methods. In the case of [PERSON] et al. 's method [19], some blocks at the boundary of the tampered region were erroneously identified. [PERSON] et al. 's method [23] showed that the quality of the recovered image was high when the tampered domain was less than 35% of the entire image. [PERSON] et al. 's method did the authentication bit and reference bit in the three LSB layers of the image. Therefore, the restored image was excellent under limited conditions. [PERSON] & [PERSON] [27] produced an index table of the original image through vector quantization (VQ), and the obtained data were hidden in the cover image for image restoration. If the VQ is lost with a tamper attack, the restoration

Figure 7: Comparison of the performance between previous methods and our proposed method. of the lost VQ area is impossible. In [PERSON] et al.