# Enhanced Joint and Separable Reversible Data Hiding in Encrypted Images with High Payload
## 5 Experimental Results and Discussion
### Separable System  
The test image Jet sized 512 \(\times\) 512 shown in Figure 15a is used as the original image in the experiment of separable system. After image encryption, we embed 16,384 bits into the encrypted image by setting \(t=8\). That means we have embedded the information bits into the most significant bits of selected pixels. With an encrypted image containing information bits (Figure 15b), we can extract the information bits without any error using the data-hiding key. If we directly decrypt the encrypted image containing information bits with the encryption key and filter the directly decrypted image using a median filter, then, we get a filtered decrypted image, as given in Figure 15c. By exploiting  
Figure 14: BER comparison between the proposed system and the referenced systems for the test image Sailboat. (**a**) Comparison of systems mentioned. (**b**) Comparison of proposed system and Wu and Sun.  
Figure 13: BER comparison between the proposed system and the referenced systems for the test image Peppers. (**a**) Comparison of systems mentioned. (**b**) Comparison of proposed system and Wu and Sun.  
both the data-hiding and the encryption keys, the embedded data can be successfully extracted and the original image can be perfectly restored from the encrypted image containing information bits. The restored image is demonstrated in Figure 15d.  
To evaluate the performance of the separable system, extensive experiments are conducted, as illustrated in Table 5. In the separable method, all the embedded bits are extracted without any error. As a result, bit error rate of the extracted data is 0, and it is not mentioned in the table. In Table 5, we compare the peak signal-to-noise ratio (PSNR(dB)) of the recovered image between the proposed system and the referenced systems (based on embedding rate) for test images, Lena, Jet, Peppers, and Sailboat. For test image Lena (Table 5), the original image can be losslessly recovered for all the embedding rates by the proposed system and [PERSON] and [PERSON] system [20]. However, PSNR in [PERSON]'s system [21] is 44.65 dB when embedding rate is 0.1563 bpp which is significantly lower than the proposed system. For Jet and Peppers images (Table 5), complete reversibility is provided by the proposed system. However, these test images cannot be recovered to the original ones by [PERSON]'s [21] and [PERSON] methods [20] for the demonstrated embedding rates. For the Sailboat image (Table 5), PSNR of the proposed system is 57.16 dB when 40,960 bits are embedded which is higher than other systems. That means, except the Sailboat image, the proposed separable system obtains complete reversibility especially when high embedding rates are used. As our proposed image restoration is based on spatial correlation of natural images, the Sailboat image due to the weak spatial correlation shows worse performance than other test images, especially when the embedding rate is high. It can be seen that the smoother the test image, the better the performance of image recovery is. When the embedding rate is 0.0625 for most test images, the original image can be successfully recovered. One of the techniques to guarantee small error probability over any circumstances, especially for weak correlated images, is to use data hiding systems with smaller embedding rates. However, there is a trade-off relation between embedding rates and performances.  
Figure 15: Experiment by separable system. (**a**) Original Jet; (**b**) encrypted Jet containing information bits; (**c**) filtered decrypted Jet containing information bits; and (**d**) recovered Jet.