Reversible Data Hiding in JPEG Grayscale Images in Compressed Domain

JPEG is one of the most widely used image compression formats, and applying reversible data hiding (RDH) techniques to verify the authenticity and integrity of JPEG images is of significant importance. Over the past years, various RDH algorithms have been proposed for JPEG images, which enhance performance through adaptive strategies such as block sorting and frequency selection. To reduce computational overhead, this paper proposes a novel RDH method in the compressed domain of JPEG images based on a two-dimensional histogram strategy. A dual-sorting mechanism is introduced to generate a more accurate block ranking sequence. During the embedding phase, secret data is embedded by pairing adjacent DCT coefficients as coordinate values. Smoother blocks are preferentially selected for data hiding to minimize distortion. Experimental results demonstrate that the proposed two-dimensional histogram embedding scheme achieves higher embedding capacity with minimal visual distortion caused by the dual sorting process. Moreover, the embedding and extraction procedures are computationally efficient, making the method suitable for practical engineering applications.