## 2 Literature Review
### Detailed Review of [PERSON] and [PERSON]'s TLE Scheme [30]  
In 2020, [PERSON] and [PERSON] [30] discussed the RRDH scheme using two-layer embedding (TLE) strategy. The TLE scheme provides good resistance against the minor altercations while providing high embedding capacity with decent quality stego-image. First, [PERSON] and [PERSON]'s scheme decomposes the cover image into two planes, namely the most-significant-bit (MSB) and least-significant-bit (LSB) planes, by separating the user-defined number (\(n\)) of LSBs from all of the bits in each pixel of the image. It is obvious that each pixel \((P_{i,j})\) of the image is represented by eight bits as its value ranges from 0 to 255. The pixel \((P_{i,j})\) is decomposed into the MSB and LSB planes using the following equations:  
\[P_{i,j}=\sum\
olimits_{k=0}^{n-1}b_{k}*2^{k}+\sum\
olimits_{k=n}^{7}b_{k}*2^{k} \tag{1}\]  
where  
\[P_{i,j}^{LSB}=\sum\
olimits_{k=0}^{n-1}b_{k}*2^{k} \tag{2}\]  
\[P_{i,j}^{MSB}=\sum\
olimits_{k=n}^{7}b_{k}*2^{k} \tag{3}\]Here, \(P_{i,j}^{LSB}\) and \(P_{i,j}^{MSB}\) represent the LSB and MSB planes, respectively, for \(P_{i,j}\) and \(b_{k}\ \epsilon\ \{0,\ 1\}\) represents the \(k\)th bit value of 8-bit binary representation of \(P_{i,j}\). By processing each pixel of the cover image (\(I\)), two images \(I^{LSB}\) and \(I^{MSB}\) are obtained. To provide resistance against minor modifications, the TLE scheme embeds the secret information in the MSB plane. The image \(I^{MSB}\) is represented in a checkboard pattern so that two independent sets of pixels--x-set in saffron and \(y\)-set in white--can be obtained as shown in Figure 1. Next, the \(x\)-set pixels are scanned and sorted according to their local complexity. The pixels are arranged into the ascending order of their complexity so that the pixels with the least complexity can be preferred for embedding the information. The preference helps in limiting the distortion, as the pixels with a lower local complexity are probably the most expanded, whereas higher-local-complexity pixels are probably the most shifted, thus causing undesired distortion. Next, the TLE scheme embeds the secret information in each pixel of the image into two layers by using the PEE strategy. In the first layer, the pixel (\(P_{i,j}^{HSB}\)) is predicted and an error (\(e_{1\ i,j}^{HSB}\)) is calculated as follows:  
\[e_{1\ i,j}^{HSB}=\ P_{i,j}^{HSB}-\hat{\mathrm{P}}_{1\ i,j}^{HSB} \tag{4}\]  
where \(\hat{\mathrm{P}}_{1\ i,j}^{HSB}\) is the predicted pixel value determined using a selected predictor from the first set of given set of predictors. Next, the secret data bit \(S_{1}^{D}\epsilon\ \{0,\ 1\}\) is embedded using Equation (5) as follows:  
\[P_{i,j}^{MSB}= \begin{cases}P_{i,j}^{MSB}+S_{1}^{D}\ \text{if}\ e_{1\ i,j}^{HSB}=1,\\ P_{i,j}^{MSB}+1\ \text{if}\ e_{1\ i,j}^{HSB}>1,\\ P_{i,j}^{MSB}\ \text{if}\ e_{1\ i,j}^{HSB}<1.\end{cases}  \tag{5}\]  
Here, \(P_{i,j}^{MSB}\) is the marked pixel obtained after the first layer of embedding. To again embed the secret information bits in the pixel, another error (\(e_{2\ i,j}^{HSB}\)) is calculated using Equation (6) after the predicted pixel value determined using a selected predictor from the second set of given set of predictors. \[e_{2\ i,j}^{HSB}=\ P_{i,j}^{HSB}-\hat{\mathrm{P}}_{2\ i,j}^{HSB} \tag{6}\]  
Next, the secret data bit \(S_{2}^{D}\epsilon\ \{0,\ 1\}\) is embedded using Equation (7). It is to be noted whether the second-layer-predicted pixel value \(\hat{\mathrm{P}}_{2\ i,j}^{HSB}\) is equivalent to the first-layer one. In  
Figure 1: Checkboard representation of image. other words, \(\hat{\rho}_{1\,i,j}^{HSB}\) then \(\hat{\rho}_{1\,i,j}^{HSB}\) are increased by one so that secret bits can be embedded into the pixels optimally. \[P_{i,j}^{\prime\,MSB}=\left\{ \begin{array}{l}P_{i,j}^{\prime\,MSB}-S_{2}^{D}\ \text{if}\ e_{2\,i,j}^{HSB}=-1,\\ P_{i,j}^{\prime\,MSB}-1\ \text{if}\ e_{2\,i,j}^{HSB}<-1,\\ P_{i,j}^{\prime\,MSB}\ \text{if}\ e_{2\,i,j}^{HSB}>-1.\end{array} \right.