# Enhanced Dual Reversible Data Hiding Using Combined Approaches
## 1 Introduction
The main purpose of SS is to enhance data security and ensure that even if secret data are leaked, the original data cannot be reconstructed from only a portion of the pieces. [PERSON] et al. (2007) [15] proposed a dual image-based RDH method using the Exploiting Modification Direction (EMD) [30] technique. The EMD technique optimizes image quality by inserting data using the modification direction of each pixel, which allows for achieving high PSNR (Peak Signal-to-Noise Ratio) values. However, there is a potential issue of quality differences occurring between the two generated images. [PERSON] et al. (2024) [27] proposed a method to optimize the LSB matching revisited [31] technique and the dual RDH method based on EMD by [PERSON] et al. (2006) [15]. [PERSON] and [PERSON] (2013) [16] also converted secret data into base 5 secret symbols. Every two continuous secret symbols were referred as a group for embedding in an identical pixel pair. The reversibility was fulfilled by the orientation combination of pixel pairs in dual stego-images. [PERSON] et al. (2015) [17] introduced a dual image-based RDH technique using LSB (least significant bit) matching. This technique uses seven rules to conceal pixel modificationsand maintains high hiding capacity and image quality. By generating two stego images, it can effectively hide secret data and restore the original image after data extraction. [PERSON] et al. (2015) [18] introduced a dual image-based RDH scheme using a Sudoku reference matrix. [PERSON] et al. took the initiative to take a grayscale image as the secret data. Each pixel in the secret image was first converted into three base 9 numeral symbols, and then three symbols were concealed in a cover pixel pair to generate two stego pixel pairs with the help of the Sudoku reference matrix. Though a higher embedding ratio (ER) of 2 bpp could be achieved in their scheme, the image quality of each stego image was only about 36 dB. [PERSON] et al. (2017) [19] improved the dual image RDH technique by using a strategy of selecting movable pixel coordinates with minimal distortion. This method generates two stego images and maintains high image quality by minimizing distortion during data insertion. This approach is particularly useful when dealing with sensitive data such as medical images and can achieve high PSNR values. [PERSON] and [PERSON] (2020) [22] used the same idea as [PERSON] and [PERSON] [16], but their embedding ratio reaches to 1.14 bits per pixel. Matrix encoding (ME), discovered by [PERSON] [32] in 1998, demonstrates excellent performance in terms of embedding efficiency for DH. [PERSON] first implemented ME in his F5 steganography [33] algorithm. To enhance the F5 algorithm's efficiency for lengthy messages, [PERSON] et al. (2001) [34] proposed random linear codes. Bose-Chaudhuri-Hocquenghem (BCH) codes [35] were later applied to achieve an optimal balance between embedding complexity and efficiency. [PERSON] et al. (2006) [36] proposed an efficient data hiding method utilizing the error detection and correction capabilities of Hamming code (HC). Later, in 2009, they introduced an advanced data hiding technique called Hamming + 1 DH (H1 DH) [37], which maximized performance. This technique extends the fundamental principles of HC to allow for the hiding of larger amounts of data. H1 DH offers superior embedding efficiency compared to matrix encoding based on Hamming coding. While matrix encoding is efficient, it falls short of theoretically achievable bounds for payloads exceeding 67% of embedding capacity. LSB substitution-based DH schemes can achieve high embedding capacity. In this study, we propose a method to maximize dual RDH performance by integrating HC with arithmetic coding (AC) compression techniques [38; 39; 40]. Our approach utilizes two duplicate grayscale images derived from the original cover image. While HC is effective in data encoding and error correction, it has inherent limitations in embedding large amounts of data and lacks robustness as a standalone RDH solution.