# Enhanced Dual Reversible Data Hiding Using Combined Approaches
## 4 Experimental Results
The proposed scheme consistently achieved an embedding ratio of 1.5 across all tested images, which surpasses the performance of existing methods. In contrast, methods by [PERSON] et al. [15], [PERSON] et al. [16], [PERSON] et al. [22], and [PERSON] et al. [20] achieved ER values ranging from 1.0 to 1.14, highlighting the superiority of the proposed approach in terms of data hiding capacity. The consistent results across all images demonstrate the robustness and adaptability of the proposed method to various image types. The results emphasize that the proposed method significantly increases the embedding capacity while maintaining image fidelity. This improvement suggests that the technique can be effectively applied in applications where high-capacity and reversible data hiding are crucial, such as secure communication, medical imaging, and digital forensics. Additionally, the stability of the achieved ER values across different images further validates the reliability of the proposed approach in practical scenarios. Overall, the experimental findings confirm that the proposed RDH method offers a competitive advantage over existing approaches [15; 16; 20; 22], making it a promising solution for high-capacity data embedding applications. Table 2 presents the average PSNR values of nine test images for each shadow generated using the comparative methods when embedding 5000, 10,000, and 20,000 bits of data. The results demonstrate that the proposed scheme achieves a superior PSNR in most shadow images compared to other methods. To ensure a fair evaluation, only dual image RDH methods were selected for comparison. The studies included meet the following criteria:  
* Dual image RDH methods were chosen to maintain consistency with the proposed approach and avoid unfair comparisons with Single-Image RDH techniques. * Well-cited and representative studies in the field were selected to highlight key advancements and distinctions. * Studies providing PSNR, SSIM, and ER metrics were included to enable an objective performance comparison. Among the existing approaches, [PERSON] et al. [20] and [PERSON] et al. [26] achieved the highest PSNR values, apart from our proposed method. [PERSON] et al. 's [26] approach improves the data hiding efficiency by embedding and extracting data using a vector coordinate transformation (TOC) approach without requiring a codebook. This method minimizes unnecessary additional data storage and reduces distortions, leading to higher PSNR values. As a result, it effectively balances high embedding capacity and image quality preservation. On the other hand, the methods proposed by [PERSON] et al. [23] and [PERSON] et al. [25] achieved maximum PSNR values of 61.25 dB and 65.33 dB, respectively, which are relatively lower than those of the methods compared in Table 2.  
While our method already demonstrates significant PSNR improvements over previous approaches, further PSNR optimization remains a crucial research objective. Although a PSNR above 30 dB is generally considered to be visually imperceptible, optimizing the PSNR is still essential for data hiding research. A higher PSNR is particularly critical in applications requiring high-fidelity image quality, such as medical imaging, forensic analysis, and security-sensitive environments. Additionally, recent advancements in AI-based steganalysis suggest that higher PSNR values can reduce the likelihood of detection, making data hiding techniques more robust against automated detection systems. Furthermore, increasing the PSNR while maintaining a high ER presents a technical challenge, and our method demonstrates that high-quality data hiding can be achieved without compromising capacity. Therefore, PSNR optimization in this study is not merely aimed at surpassing 30 dB but rather at maximizing the applicability of the proposed method across different domains while enhancing its resistance to detection. Regular-Singular (RS) analysis [45] is a statistical method used to evaluate the detectability or quality changes resulting from data hiding in images.