## 4 Experimental Results and Discussion  
In Section 3, we proposed AMBTC-based SRDH-EI, and in this section, we describe in detail the comparison and analysis of the simulation results to verify the performance of the proposed method. The computing platform used in the experiment has a Core i5-8250U processor, 1.60 GHz speed, 8 GB RAM, and the software for the simulation is MATLAB R2019b. The standard USC-SIPI image database [32] was used for experiments on the proposed model. Among them, some of the original \(512\times 512\) grayscale images were used for the experiment. Figure 4 shows a series of test images (e.g., Lena, Pepper, Airplane, Boat, Goldhill, Couple, Baboon, Zelda) used in the experiment. SSIM (Structural Similarity Index Metric) and PSNR (Peak Signal-to-Noise Ratio) were used for evaluation. The quality of the reconstructed image with data was measured as PSNR and defined as  
\[PSNR=10 log_{10}\frac{255^{2}}{MSE}. \tag{18}\]  
PSNR is calculated as \(10 log_{10}\) (signal power/noise power), and signal power and noise power are calculated using peak power. Here, \(255^{2}\) is the allowable pixel intensity. The MSE used for PSNR is the difference in mean intensity between the marked image and the reference image, and the lower the MSE value, the better the image quality can be  
Figure 4: Nine test images: (**a**) Baboon, (**b**) Barbara, (**c**) Boat, (**d**) Goldhill, (**e**) Airplane, (**f**) Lena, (**g**) Peppers, (**h**) Tifany, (**i**) Zelda (\(512\times 512\)). evaluated. That is, MSE is the mean of squared errors \((g_{i}-g_{i}^{\prime})^{2}\), where \(g_{i}\) and \(g_{i}^{\prime}\) are the reference image and the distorted image, respectively. MSE is calculated as follows:  
\[MSE=\frac{1}{N\times N}\sum_{i=1}^{N^{2}}(g_{i}-g_{i}^{\prime})^{2} \tag{19}\]  
In addition, another measurement introduced for performance evaluation is SSIM, which is a formula (Equation (20)) that measures the similarity between the original image and the marked image. \[SSIM(g,g^{\prime})=\frac{(2\mu_{g}\mu_{g^{\prime}}+c_{1})(2\sigma_{gg^{\prime} }+c_{2})}{(\mu_{g}^{2}+\mu_{g^{\prime}}^{2}+c_{1})(\sigma_{g}^{2}+\sigma_{g^{ \prime}}^{2}+c_{2})} \tag{20}\]  
where \(\mu_{g}\) and \(\mu_{g^{\prime}}\) are the mean values of \(g\) and \(g^{\prime}\), respectively, and \(c_{1}\) is the stabilization constant and \(\sigma_{g}^{2},\sigma_{g}^{\prime 2}\), and \(\sigma_{gg^{\prime}}\) are the variances and covariances of the cover image and the stego image. \(c_{1}\) and \(c_{2}\) are constant values to avoid division by zero problems. Table 1 compares the PSNR and SSIM measurements for the cover image, the encrypted image, and the encrypted image when the difference between the two quantization levels is \(T=5\). First, it shows the PSNR and SSIM measurements between AMBTC-compressed images for the original image. The PSNRs of Baboon and Barbara are 26.9765 and 27.0756, which are measured below 30 dB. Baboon is a high-frequency image, and when compressed with AMBTC, the SSIM is z 0.8872 image, which is not classified as bad for the human visual system. It can be seen that the Zelda image has the highest PSNR of 36.6537. The PSNR and SSIM of the encrypted AMBTC are 10 or less and 0.0159 or less, respectively. For this reason, it can be seen that the encrypted image is encrypted to such a level that it is difficult to infer the original image from the encrypted image. For the encrypted image, data were hidden by the proposed method with two quantization levels \(T=5\). When looking at the PSNR and SSIM measurements of the decoded AMBTC including the data, it can be confirmed that it is almost similar to the cover AMBTC. That is, PSNR and SSIM are acceptable even if enough data is concealed. Figure 5 shows the encrypted image mentioned in Table 1, and data hiding is applied to the encrypted image and transmitted to the receiver. The receiver cannot know the existence of the data and the form of the image from this encrypted image. This is the advantage of encryption RDH.