## 4 Experimental Studies  
This section presents comparisons and experimental results of our proposed method. The proposed algorithm is tested on a series of standard colored and grayscale cover images to evaluate by the data hiding measurement metrics such as embedding capacity (EC), payload (P), and peak signal-to-noise ratio (PSNR). The article also presents histogram analysis, Regular Singular (RS) analysis and pixel distributions for the security tests of the proposed method. We tested our proposed method with many images in the USC-SIPI dataset [39] that is a collection of digitized images. This dataset is utilized to support research in image processing, image analysis, and image steganography. Figure 6 presents four \(512\times 512\) grayscale original cover images, which are utilized to embed secret data with diverse data hiding capacity in the experimental studies. Also, the secret data, by the computer randomly generates, are embedded into these original cover images in the experiments. In addition, experimental studies have been carried out on the same color cover images of \(512\times 512\) sizes to demonstrate the validity of the algorithm. The PSNR value is utilized to measure the similarity between the original cover image and the stego image. The higher this value, the better the stego image quality. Formulas showing the calculation of the mean square error (MSE), which is between the original cover image and the stego image, and PSNR values are calculated in (16) and (17), respectively. The H and W values represent the size of the cover image in (16). \[\text{MSE}=\frac{1}{\text{H}\;\times\;\text{W}}\;\sum_{i=1}^{\text{H}}\sum_{j= 1}^{\text{W}}(C(i,j)-S(i,j))^{2} \tag{16}\]  
\[\text{PSNR}=10\times\text{log}_{10}\;\frac{255^{2}}{\text{MSE}} \tag{17}\]  
The embedding capacity (EC) is expressed as the total secret data bits that are embedded into two stego images, while the payload (P) value in (18) represents that hidden secret data bits per pixel. \[\text{P}=\frac{\text{EC}}{2\times\;\text{H}\;\times\;\text{W}} \tag{18}\]  
Table 3 presents a comparison of embedding capacity and PSNR value of different stego images for \(n=1\). As can be seen from experimental studies, when 100% secret data is in hidden on different cover images, the PSNR values of stego image 1 and stego image 2  
Figure 6: The flow chart of the data extraction process. (**a**) Lena; (**b**) Airplane; (**c**) Peppers; (**d**) Baboon. Figure 7 indicates average embedding capacity and PSNR values for \(n=1\) to \(5\) in all grayscale images used in experimental studies. In the proposed algorithm, it is seen from the graph that the highest PSNR values are obtained for \(n=1\) and the maximum payload value is acquired for \(n=5\). Table 8 gives the table presenting the comparison of payload, embedding capacity and PSNR values for colored cover images. When \(n=1\), the PSNR value is more than \(51\) (dB) and up to \(1\),\(561\),\(416\) bits of secret data can be embedded. When \(n=4\), the PSNR value is more than \(34\) (dB) and up to \(3\),\(847\),\(636\) bits of secret data can be embedded, which is the most appropriate relationship between embedding capacity and PSNR in this study. When \(n=5\), the embedding capacity increases significantly, but it is observed that the PSNR value is lower than acceptable (\(30\) dB). The speed tests of the proposed method for data hiding and extraction are presented in Table 9. For \(n=1\) and \(5\), the random secret data generated by the computer were hidden and extracted into different grayscale cover images in speed test studies. When the speed tests performed are examined, it is seen that data hiding and extraction times are close to each other and are measured in milliseconds. It has been observed that with the increase in the payload, the times of data hiding and extraction increase.