# Enhanced Joint and Separable Reversible Data Hiding in Encrypted Images with High Payload
## 2 Related Work
Then, the decrypted image is divided into two sets: \(T_{\text{Qual}}\) and \(T_{\text{Forb}}\). The pixels in \(T_{\text{Qual}}\) are retrieved and divided into groups, and the \(d\)-th group contains \(m\) pixels, denoted as \(P(u,d)\) for \(u=1,\,2,\ldots,\,m\). For each pixel, an estimated pixel, \(P_{\text{Est}}(u,d)\), is calculated by using four neighboring pixels and a flipped pixel, \(P_{\text{Flip}}(u,d)\), is determined by flipping the \(t\)-th bit of \(P(u,d)\). Then, for the smoothness calculation, the prediction error \(PE\) and flipped prediction error \(PE_{\text{Flip}}\), respectively, are calculated by using the following equations:  
\[PE(d) = \sum_{u=1}^{m}\left|P_{\text{Est}}(u,d)-P(u,d)\right| \tag{3}\] \[PE_{\text{Flip}}(d) = \sum_{u=1}^{m}\left|P_{\text{Est}}(u,d)-P_{\text{Flip}}(u,d)\right| \tag{4}\]  
The estimated values in the prediction error in (3) and (4) are not good metrics, since the estimated value is different from the actual value. The smoothness calculation from using the prediction error leads to a worsened bit error rate. For this calculation, it is required to estimate the selected pixel by using four neighboring pixels of that pixel before calculating the prediction error. If the neighboring pixels are changed during the data embedding process, the pixel estimation will be failed and the prediction error calculation will be unsuccessful too. For example, let us consider the Figure 1a,b as the original image and embedded image, respectively. From Figure 1b, it is seen that some pixels and their neighboring pixels are changed due to embedding data. In this circumstance, the pixel from the neighboring pixels cannot be estimated accurately. For instance, let pixel 0 at position (5, 2) (Figure 1b) be the selected pixel. As their neighboring pixels [26; 13] are also changed, so it is not possible to estimate the value of that pixel from the neighboring pixels. So, the main constraint of prediction error is that the neighboring pixels cannot be changed which ultimately decreases the embedding rate. Therefore, in the proposed work, to reduce the bit error rate and increase the embedding rate, we use the absolute difference of neighboring pixels, instead of prediction error, for the smoothness calculation for both joint and separable methods. In [21], [PERSON] introduced a separable RDH-EI method where the encrypted bits are compressed to accommodate the additional bits, \(S\). Using a data-hiding key, the data-hider pseudo-randomly permutes and divides the encrypted image into groups with size of \(L\). The \(M\) LSB-planes of each group are compressed with a matrix sized (\(M\)-\(L\)-\(S\)) \(\times\) (\(M\)-\(L\)) and vacated room is used to embed data. As the additional bits are embedded in LSBs of the encrypted images, they can be extracted directly from the encrypted marked image by using a data-hiding key. On the receiver side, the marked encryptedimage is decrypted and a total of 8-\(M\) most significant bits (MSB) of pixels are obtained. The receiver then estimates the \(M\) LSBs by the MSBs of neighboring pixels. By comparing the estimated bits with the vectors in the coset corresponding to the extracted vectors, the receiver can recover the original bits of the \(M\) LSBs. However, [PERSON]'s technique is little complicated and data cannot be extracted precisely and the original image cannot be recovered perfectly especially when the payload is high.