# Dual Partial Reversible Data Hiding Using Enhanced Hamming Code
## 4 Experimental Results and Discussions  
In this section, we present the experimental evaluation of the proposed partial reversible data hiding (PRHB) method based on the enhanced HC(7,4) Hamming code. The primary objective of the experiments is to demonstrate the feasibility and advantages of the proposed technique through comprehensive simulations. All experiments were conducted on a system equipped with a Core i5-8250U processor (1.60 GHz) and 8 GB of RAM, utilizing Matlab R2019b as the simulation platform. This study aims to improve both embedding capacity and image quality through a dual-image RDH scheme. The proposed approach addresses prior limitations by incorporating structured virtual pixel construction and optimized codeword selection. Unlike conventional RDH, our design avoids side-information overhead and achieves near-constant embedding performance across all tested images. The improvements introduced in the data embedding process can be summarized as follows:  
* Optimized Virtual Pixel Construction: Virtual pixels are generated from two cover images to enhance error correction performance. * Complete Data Recovery Without Auxiliary Information: The embedded data can be perfectly extracted without the need for any additional side information. * Adaptive Tradeoff Between Embedding Capacity and Visual Distortion: The method employs an adaptive adjustment strategy to maintain a balance between data embedding rate and image quality. * High Stego Image Quality: The visual quality of the stego images is preserved, as quantitatively measured by the peak signal-to-noise ratio (PSNR) [2]. To objectively evaluate the performance of the proposed method, extensive experiments were carried out using nine standard 512 \(\times\) 512 grayscale images from the USC-SIPI dataset [30] (Figure 4). The evaluation metrics included embedding capacity (EC), embedding rate (ER, measured in bits per pixel, bpp, Equation (7)), and PSNR. By comparing these metrics with those achieved by conventional dual-image-based RDH methods, the superiority of the proposed scheme in terms of both capacity and visual quality is clearly demonstrated. The embedding rate (ER) is defined by Equation (7):  
\[ER=\frac{C}{2\times N\times N}(bpp). \tag{7}\]  
Figure 4: Test images: (**a**) Elaine, (**b**) Boat, (**c**) Peppers, (**d**) Goldhill, (**e**) Baboon, (**f**) Zelda, (**g**) Barbara, (**h**) Airplane, and (**i**) Couple (512 \(\times\) 512). The PSNR [2] is widely employed as an objective metric to evaluate the quality of marked images. It quantifies the difference between the reference image and the distorted (or marked) image in a logarithmic scale. The PSNR is defined by Equation (8):  
\[PSNR=10\log_{10}\left(\frac{255^{2}}{MSE}\right) \tag{8}\]  
where \(255^{2}\) represents the square of the maximum possible pixel value in an 8-bit image. The mean squared error (MSE), provided by Equation (9), measures the average squared intensity difference between corresponding pixels of the original and marked images:  
\[MSE=\frac{1}{N\times N}\sum_{i=1}^{N\times N}(x_{i}-x_{i}^{\prime})^{2}. \tag{9}\]  
In this expression, \(x_{i}\) and \(x_{i}^{\prime}\) denote the pixel values of the original and marked images at position \(i\), respectively. The error term \(e=(x_{i}-x_{i}^{\prime})^{2}\) reflects the squared deviation at each pixel. A lower MSE value indicates smaller distortion, leading to a higher PSNR value, which implies better perceived image quality. Typically, for 8-bit images, PSNR values for acceptable lossy compression range from 30 dB to 50 dB. A higher PSNR generally correlates with improved visual fidelity. Table 1 presents a comparative analysis of PSNR values for cover images (#1 and #2) and stego images (#1 and #2) when embedding 10,000 bits using the enhanced HC(7,4) PRDH method. The evaluation focuses on three key PSNR measurements:  
* PSNR(CI\(-\)OI): The PSNR between the original image (OI) and the cover image (CI), indicating the degree of modification introduced by the cover image generation process.