# Dual Partial Reversible Data Hiding Using Enhanced Hamming Code
## 1 Introduction
However, because direct application was not feasible, they devised seven new rules for pixel recovery and applied them to the dual-image restoration process. They then demonstrated the effectiveness of their proposed method through experiments. In a separate work, [PERSON] et al. (2015) [18] introduced a dual-image-based data hiding strategy utilizing a center folding technique. In this approach, secret data values are first compressed using the folding strategy, allowing more data to be embedded. The folded secret data are then hidden across two stego image pixels. Building on this, [PERSON] et al. (2017) [19] focused on improving the visual quality of stego images by identifying and enhancing areas where [PERSON]'s [18] method could be further optimized. [PERSON] et al. (2018) [21] proposed a method that extracts seven-pixel blocks from the original image and duplicates them into two arrays. The least significant bits (LSBs) of each array are adjusted using odd parity, increasing error resilience during transmission. Secret message bits are embedded into specific positions within these arrays while deliberately excluding certain predesignated positions reserved for integrity checks. During the embedding phase, bit modifications may introduce errors, which are subsequently detected and corrected by the receiver using Hamming (7,4) error correction codes. While this method demonstrates innovative integration of error-correcting codes, its low embedding capacity (0.21 bpp) limits its suitability for applications requiring high payloads. [PERSON] and [PERSON] (2021) [23] introduced a dual-image RDH scheme utilizing the exploiting modification direction (EMD) method, achieving reversibility without additional overhead. While their method represents an improvement in eliminating auxiliary data, it falls short of surpassing earlier EMD-based methods such as that of [PERSON] et al. (2013) [14]. In addition, it involves complex orientation combinations, which increase implementation complexity and make optimization difficult. [PERSON] and [PERSON] (2024) [26] proposed a novel dual-image RDH method based on vector coordinates with triangular order coding (TOC), achieving superior embedding capacity and image quality without requiring additional side information. Their method focuses on position-based embedding, allowing for flexible adjustment of capacity via the \(k\) parameter. [PERSON] et al. (2025) [27] proposed a multi-party RDH framework for medical information that utilizes texture-guided hierarchical quantization coding (TGHQC) to enhance embedding capacity and security. Additionally, both image owners and data providers perform data embedding through a dual embedding mechanism, allowing for role-specific data access. This method maintains data reversibility and security, thereby improving the efficiency of medical information management. [PERSON] et al. (2024) [28] proposed a reversible fragile watermarking scheme based on the insect matrix reversible embedding algorithm to enable full recovery of untampered cover images. Upon tampering, adaptive dual recovery schemes are employed to restore corrupted data while maintaining high image quality. Moreover, image-rendering techniques are introduced to enhance the accuracy of tampering detection, particularly in cases of tampering coincidence. This study proposes an enhanced dual-image RDH method based on the HC(7,4) Hamming code to overcome limitations in prior methods. By applying this Hamming code to pixel groups across two cover images, our method significantly increases embedding capacity, reaching 1.5 bpp, which is over seven times greater than in [PERSON] et al. (2018) [21]. In addition, our method ensures high visual quality with PSNR values between 48 and 49 dB, outperforming methods such as that of [PERSON] et al. (2013) [14]. Compared to complex EMD-based design of [PERSON] and [PERSON] (2021) [23], our scheme offers a simpler and more efficient solution.