## 4 Experimental Results
### Image Steganalysis  
In general, steganalysis for the stego image cannot be judged by the human eye. Because the stego image's quality is more than \(33\) dB, the human eye is unable to detect if the stego image has secrets or not. Therefore, it is necessary to have an effective way to detect whether a secret message is embedded. For image steganalysis, the regular singular steganalysis (RS steganalysis) is a common method to detect the stego image. In this paper, in order to prove that our proposed scheme has good security, we propose this detection method to test the stego image generated by our scheme. In RS steganalysis, \(n\) adjacent pixels \((x_{1},x_{2},\ldots,x_{n})\) are selected as a pixel group. Then, the discrimination function \(DF\), defined as \(DF(x_{1},x_{2},\ldots,x_{n})=\sum_{i=1}^{n}|x_{i+1}-x_{i}|\), is applied to quantify the smoothness or regularity of each pixel group. The flipping function of RS steganalysis is used to define three types of pixel groups: regular (R), singular (S) and unusable (U). The percentages of all groups of regular and singular with masks \(M=[1001]\) and \(-M=[-100-1]\) are represented as \(R_{m}\), \(R_{-m}\), \(S_{m}\) and \(S_{-m}\). The statistical hypotheses of RS steganalysis are \(R_{m}\cong R_{-m}\) and \(S_{m}\cong S_{-m}\), meaning the test image can pass steganalysis. In other words, \(R_{m}\) overlaps with \(R_{-m}\), and \(S_{m}\) overlaps \(S_{-m}\). Using the RS steganalysis method, we test a method based on LSB and our proposed method. The simulation results are shown in  
Figure 7: PSNR comparison result.  
Figure 8. According to Figure 8a to 8d, the distribution of \(R_{m}\cong R_{-m}\) and \(S_{m}\cong S_{-m}\) for our proposed scheme is normal, but \(1\)-LSB, \(2\)-LSB and \(3\)-LSB denote hidden information; because the \(1\)-LSB, \(2\)-LSB and \(3\)-LSB methods mean that the secret message was hidden in the position of \(1\)-LSB, \(2\)-LSB and \(3\)-LSB for each cover image's pixel, respectively. In addition, we evaluate our proposed method with the modern steganalysis tool SPAM (subtractive pixel adjacency matrix) [19]. For the SPAM test, we use \(500\) image data from [20]. There are \(250\) cover images and \(250\) stego images used for training. The test results between minimizing the power of the optimal detector (MiPOD) [21] and our proposed scheme are shown in Figure 9. The MiPOD scheme was proposed by [PERSON] _et al._ in 2015. The major contribution of the MiPOD scheme is that the pixel values are changed by at most \(\pm 1\) when a secure message is embedded into the cover image with the Gaussian cover model [22, 23], and [PERSON] _et al._ also considered a novel detectability-limited sender and estimated the secure payload of each cover image. In Figure 9, the vertical axis represents the error rate obtained by the SPAM method, and the horizontal axis represents the embedding rate (bpp), which ranges from \(0.1\) bpp to \(6.7\) bpp. From Figure 9, we can find that the error rate of the proposed method is better than the MiPOD scheme when the embedding capacity is over 0.6 bpp. In comparison, the proposed method has a higher embedding rate and a lower error rate. Therefore, if we can adapt the secret data embedding rate (such as MiPOD scheme); this can provide a certain probability to avoid detection attack. Furthermore, to understand steganalysis and stego image security, the spatial rich model (SRM) [24] or maxSRM [25] method can be used to analyze the proposed method in the future.  
Figure 8: RS steganalysis. (**a**) Proposed scheme; (**b**) \(1\)-least significant bit (LSB); (**c**) \(2\)-LSB; (**d**) \(3\)-LSB.