# Analysis of New Orthogonal Transforms for Digital Watermarking
## 4 Experimental Results
### Algorithm Testing  
The main targets for the analyzed watermark algorithms are the high imperceptibility of the watermark embedded in an image, high recovery accuracy, and large capacity of the watermark. Therefore, the Peak Signal-to-Noise Ratio (PSNR) is taken as a measure of perceptual quality, and the bit error rate (BER) indicates the level of incorrectly recovered bits. The measurements of these ratios were performed for watermarks inserted in the domains of transforms listed in Section 4.2. The relation between PSNR ratio and the length of the inserted bitstream, for all the above-mentioned embedding methods and transforms, is presented in Figures 2-6 (in order to better distinguish both types of transforms, the graphs for the proposed orthogonal transforms are marked in green while for DCT in red). It can be observed that a perceptual quality of an image with a watermark embedded in the DCT spectrum is consistently better than in the case of the remaining orthogonal transforms. However, it is worth highlighting that for methods M1, M2, and M3, the BER is very poor, which means that the watermark cannot be recovered. Thus, the PSNR results in these cases need to be ignored. Only in the case of method M4 is the BER for DCT very low, so only the corresponding PSNR value may be used as a reference. Nonetheless, both transforms can provide satisfying results. It is assumed that the PSNR above 35 dB for 8-bit images indicates that the two images being compared are visually identical, with no perceptual loss of quality [20]. In most cases, such results are achieved, and a PSNR below 35 dB is observed only in case of longer bitstreams or embedding approaches, which apparently do not fit the given transform. The relation between BER ratio and the length of a hidden message, for particular embedding approaches and transforms, is shown in Figures 7-11 (in order to better distinguish both types of transforms, the graphs for the proposed orthogonal transforms are marked in blue while for DCT in red). As can be seen, some methods do not guarantee a sufficient level of accuracy during the extraction process. It is understandable in the case of Method 1 since it uses even distribution during the embedding stage. For proposed orthogonal transforms, methods 2, 3, and 5 provide adaptive embedding, which selects these blocks of spectral coefficients that should not degrade the original image and at the same time allow for almost full data recovery. The BER does not exceed 0.1% in most situations, with the total length of the watermark bitstream ranging from 1000 to 75,000 bits. When using method 4 or 5, the BER is predominantly equal to zero. The DCT approach provides the most reliable and acceptable results for method 4. This could be predicted due to the fact that this method uses a zigzag order for channel selection during the watermark insertion phase, which is specifically designed for this type of transform and is also used in JPEG compression [21]. Although a watermark inserted in the presented orthogonal transform domains seems to fit better in different embedding approaches, both transform types are useful when a large amount of information needs to be inserted into an image. Figure 3: Relation between PSNR and embedded data size for method 2 and all transform types. Figure 2: Relation between PSNR and embedded data size for method 1 and all transform types. Figure 4: Relation between PSNR and embedded data size for method 3 and all transform types. Figure 5: Relation between PSNR and embedded data size for method 4 and all transform types. Figure 6: Relation between PSNR and embedded data size for method 5 and all transform types. Figure 7: Relation between BER and embedded data size for method 1 and all transform types. Figure 8: Relation between BER and embedded data size for method 2 and all transform types. Figure 9: Relation between BER and embedded data size for method 3 and all transform types.